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## Sums over topological sectors and quantization of Fayet-Iliopoulos parameters,” arXiv:1012.5999 [hep-th

Citations: | 24 - 6 self |

### Citations

718 |
Cosmic Strings and other Topological Defects
- VILENKIN, SHELLARD
- 1994
(Show Context)
Citation Context ...ssive noninvariant fields would see that gauge transformation. Let us now turn to physical examples. The hypothetical cosmic string above sounds very similar to the Zn cosmic string discussed in e.g. =-=[61]-=-[section 4.2.2]. There, one has an SU(2) gauge theory with a pair of triplet-valued Higgs fields which are required (by virtue of a potential term) to be orthogonal. Giving the first Higgs triplet a v... |

416 |
Cohomology of quotients in symplectic and algebraic geometry
- Kirwan
- 1984
(Show Context)
Citation Context ...d in rigid supersymmetry in terms of symplectic quotients, the paper [8] argues that the structure above in supergravity can be understood in terms of ‘geometric invariant theory’ quotients (see e.g. =-=[63, 64, 65]-=-), the algebro-geometric analogue of symplectic quotients. In particular, in a geometric invariant theory quotient, the analogue of the Fayet-Iliopoulos parameter is quantized, because it is realized ... |

293 | Electric-magnetic duality and the geometric Langlands program,” hep-th/0604151
- Kapustin, Witten
(Show Context)
Citation Context ...he matter. Our first physical example will involve a topologically-nontrivial spacetime four-manifold. Consider N = 4 supersymmetric theories arising in recent work on the geometric Langlands program =-=[39]-=-. There, one compactifies a four-dimensional N = 4 theory along a Riemann surface to get a two-dimensional theory, a nonlinear sigma model whose target space is the Hitchin moduli space on the compact... |

229 |
Intersection theory on algebraic stacks and on their moduli spaces
- Vistoli
- 1989
(Show Context)
Citation Context ...literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] for a few representative examples.) Briefly, a stack is a manifold “paired with automorphisms.” (See e.g. =-=[26, 27, 28]-=- for a more technical definition.) At the same level of brevity, a gerbe is a stack in which one has the same automorphisms everywhere. Mathematically, a gerbe can be thought of locally as covered by ... |

216 |
Ruan: A new cohomology theory of orbifold
- Chen, Y
(Show Context)
Citation Context ...4, 15, 16, 17, 18] and reviewed in conference proceedings including [19, 20, 21]. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example =-=[22, 23, 24, 25]-=- for a few representative examples.) Briefly, a stack is a manifold “paired with automorphisms.” (See e.g. [26, 27, 28] for a more technical definition.) At the same level of brevity, a gerbe is a sta... |

210 |
Introduction to moduli problems and orbit spaces, Tata
- Newstead
- 1978
(Show Context)
Citation Context ...d in rigid supersymmetry in terms of symplectic quotients, the paper [8] argues that the structure above in supergravity can be understood in terms of ‘geometric invariant theory’ quotients (see e.g. =-=[63, 64, 65]-=-), the algebro-geometric analogue of symplectic quotients. In particular, in a geometric invariant theory quotient, the analogue of the Fayet-Iliopoulos parameter is quantized, because it is realized ... |

164 | Mirror symmetry in three-dimensional gauge theories
- Intriligator, Seiberg
- 1996
(Show Context)
Citation Context ... for example, [74], and there is a gerbe structure on some of the moduli spaces of the field theories discussed there. Similarly, it would be interesting to understand the three-dimensional ‘mirrors’ =-=[75]-=- to theories with nonminimally-charged electrons. In two dimensions, such mirrors turned out to involve either discrete-valued fields [13] or, equivalently, disconnected targets [14]. It would also be... |

150 |
Champs Algébriques
- Laumon, Moret-Bailly
- 2000
(Show Context)
Citation Context ...literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] for a few representative examples.) Briefly, a stack is a manifold “paired with automorphisms.” (See e.g. =-=[26, 27, 28]-=- for a more technical definition.) At the same level of brevity, a gerbe is a stack in which one has the same automorphisms everywhere. Mathematically, a gerbe can be thought of locally as covered by ... |

128 | Gromov-Witten theory of Deligne-Mumford stacks
- Abramovich, Graber, et al.
(Show Context)
Citation Context ...4, 15, 16, 17, 18] and reviewed in conference proceedings including [19, 20, 21]. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example =-=[22, 23, 24, 25]-=- for a few representative examples.) Briefly, a stack is a manifold “paired with automorphisms.” (See e.g. [26, 27, 28] for a more technical definition.) At the same level of brevity, a gerbe is a sta... |

125 | Applied Conformal Field Theory
- Ginsparg
- 1991
(Show Context)
Citation Context ... R, NS to describe states on the cylinder, but the quantum symmetry is defined by (un)twisted sectors on the complex plane, and the conformal transformation between the two exchanges R and NS sectors =-=[50]-=-[section 7.1]. 17 are massive. The quantum symmetry leaves the left-moving NS sector states invariant and multiplies the left-moving R sector states by a phase, which matches the effect of the Z2 gerb... |

116 | On orbifolds with discrete torsion
- Vafa, Witten
- 1995
(Show Context)
Citation Context ...tion of D4 on T 6. Let us take the Z2 center to act trivially, so that the D4 acts by first projecting to Z2×Z2, and then act with a standard Calabi-Yau action of Z2 × Z2 on T 6, as described in e.g. =-=[31]-=-. Since the Z2 center acts trivially, one might naively assume that the [T 6/D4] orbifold would be physically equivalent to a [T 6/Z2×Z2] orbifold. Instead, one computes that at one-loop, for example,... |

110 |
Mirror symmetry,” arXiv:hep-th/0002222 [hep-th
- Hori, Vafa
(Show Context)
Citation Context ...heory on a disjoint union of spaces, and the fact that mirror symmetry dualizes nonperturbative effects into perturbative ones. (This result was physically derived in [13] from duality for GLSM’s ala =-=[29, 30]-=-, and also independently derived in e.g. [25] from mathematical considerations.) 7 So far we have outlined how noneffective continuous group actions can lead to new physics; the same is true of finite... |

85 | Derived categories of twisted sheaves on Calabi-Yau manifolds
- Căldăraru
- 2000
(Show Context)
Citation Context ...tleties. Let us examine the second issue above, in the special case of smooth Deligne-Mumford stacks that have a (finite) gerbe structure over a smooth manifold. A twisted bundle on a space (see e.g. =-=[66, 67, 68, 69]-=-) is a bundle in which the transition functions close only up to a higher cocycle; schematically: gαβgβγgγα = hαβγ for some Cech cocycle hαβγ , where the gαβ are transition functions. Consistency requ... |

77 |
Fayet-Iliopoulos terms in string theory. Nucl. Phys
- Dine, Seiberg, et al.
- 1987
(Show Context)
Citation Context ...efold with the standard embedding. The low-energy gauge group is12 Spin(26)× U(1) Z4 . The U(1) factor is typically anomalous and Higgsed via a four-dimensional version of the Green-Schwarz mechanism =-=[54, 55]-=-, closely related to a (field-dependent, hence not directly relevant to this paper) Fayet-Iliopoulos parameter. The remaining Z2 center of Spin(32)/Z2 descends to part of the center of the group above... |

69 |
Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nuclear Phys
- Greene, Shapere, et al.
- 1990
(Show Context)
Citation Context ...homotopy of M . The effect of the gerbe is to add a BZn fiber over each point of M . Over any point of M , therefore, is a copy of BZn, which has π1 = Zn. 13For example, the stringy cosmic strings of =-=[59]-=- arise from the fact that pi1 of the moduli stack of elliptic curves is SL(2,Z). (This stack should be distinguished from its Deligne-Mumford compactification. That compactification maps onto S2, henc... |

56 | The quantum orbifold cohomology of weighted projective spaces
- Coates, Corti, et al.
(Show Context)
Citation Context ...4, 15, 16, 17, 18] and reviewed in conference proceedings including [19, 20, 21]. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example =-=[22, 23, 24, 25]-=- for a few representative examples.) Briefly, a stack is a manifold “paired with automorphisms.” (See e.g. [26, 27, 28] for a more technical definition.) At the same level of brevity, a gerbe is a sta... |

54 |
Geometric invariant theory, Third edition.
- Mumford, Fogarty, et al.
- 1994
(Show Context)
Citation Context ...d in rigid supersymmetry in terms of symplectic quotients, the paper [8] argues that the structure above in supergravity can be understood in terms of ‘geometric invariant theory’ quotients (see e.g. =-=[63, 64, 65]-=-), the algebro-geometric analogue of symplectic quotients. In particular, in a geometric invariant theory quotient, the analogue of the Fayet-Iliopoulos parameter is quantized, because it is realized ... |

43 | Towards mirror symmetry as duality for two-dimensional abelian gauge theories
- Morrison, Plesser
- 1996
(Show Context)
Citation Context ...heory on a disjoint union of spaces, and the fact that mirror symmetry dualizes nonperturbative effects into perturbative ones. (This result was physically derived in [13] from duality for GLSM’s ala =-=[29, 30]-=-, and also independently derived in e.g. [25] from mathematical considerations.) 7 So far we have outlined how noneffective continuous group actions can lead to new physics; the same is true of finite... |

34 | Derived categories of twisted sheaves on elliptic threefolds,
- Caldararu
- 2002
(Show Context)
Citation Context ...tleties. Let us examine the second issue above, in the special case of smooth Deligne-Mumford stacks that have a (finite) gerbe structure over a smooth manifold. A twisted bundle on a space (see e.g. =-=[66, 67, 68, 69]-=-) is a bundle in which the transition functions close only up to a higher cocycle; schematically: gαβgβγgγα = hαβγ for some Cech cocycle hαβγ , where the gαβ are transition functions. Consistency requ... |

32 | Geometric Origin of Montonen-Olive Duality
- Vafa
- 1997
(Show Context)
Citation Context ...e orbifold theory (though as already noted, this is not always the case). In passing, we should also mention that there may be further examples of string theories with gerby moduli spaces implicit in =-=[58]-=-, which ‘geometrically engineers’ four-dimensional theories with nonabelian gauge groups from type II compactifications on singular spaces. 20 5 Topological defects and gerby moduli spaces Recall stab... |

29 |
Quantization of Newton’s Constant in Certain Supergravity Theories,” Phys
- Witten, Bagger
- 1982
(Show Context)
Citation Context ...and cluster decomposition 35 References 47 2 1 Introduction Recently there has been much progress in understanding Fayet-Iliopoulos parameters in supergravity, generalizing work of e.g. Bagger-Witten =-=[1]-=-, see for example [2, 3, 4, 5, 6, 7, 8, 9]. In particular, the recent paper [7] argued that in the special case of linearlyrealized group actions, Fayet-Iliopoulos parameters could be interpreted as c... |

23 | Non-birational twisted derived equivalences in abelian GLSMs
- Căldăraru, Distler, et al.
(Show Context)
Citation Context ...ow abundant evidence, including all-genera partition function computations in orbifold examples [14], checks in mirror symmetry and quantum cohomology [14], applications to gauged linear sigma models =-=[15]-=-, and now checks of predictions for Gromov-Witten invariants [33, 34, 35, 36, 37, 38]. By contrast, in the four-dimensional case above, we have no independent evidence, no examples, only the arguments... |

23 | Chiral duals of nonchiral SUSY gauge theories - Pouliot - 1995 |

23 |
Superstring theory, volume I
- Green, Schwarz, et al.
- 1987
(Show Context)
Citation Context ...r the group. In the present case, the Spin(32)/Z2 heterotic string has at its first massive level states transforming in the spinor representation of Spin(32)/Z2, which is not invariant under the Z2 (=-=[48]-=-[section 6.3.1], [49][section 2.3]), exactly as needed for a gerbe description of the moduli space to be physically relevant. On the ten-dimensional heterotic string worldsheet, this proposed Z2 gerbe... |

23 |
Heterotic compactifications with principal bundles for general groups and general
- Distler, Sharpe
- 2010
(Show Context)
Citation Context ...ations are F theory compactifications on gerbes [42]. 12We can compute this as follows. We are embedding SU(3) into a Spin(6) = SU(4) subgroup, so we begin by observing that Spin(32) has the subgroup =-=[53]-=-[appendix A] Spin(26)× Spin(6) Z2 . Since the center of both Spin(26) and Spin(6) is Z4, there is only one diagonally-acting Z2 subgroup. We can describe the center of the group above as generated by ... |

23 | Nonfine moduli spaces of sheaves on K3 surfaces,
- Caldararu
- 2002
(Show Context)
Citation Context ...tleties. Let us examine the second issue above, in the special case of smooth Deligne-Mumford stacks that have a (finite) gerbe structure over a smooth manifold. A twisted bundle on a space (see e.g. =-=[66, 67, 68, 69]-=-) is a bundle in which the transition functions close only up to a higher cocycle; schematically: gαβgβγgγα = hαβγ for some Cech cocycle hαβγ , where the gαβ are transition functions. Consistency requ... |

23 |
Evaluation of the one loop string path integral
- Polchinski
- 1986
(Show Context)
Citation Context ...we perform separately. Path integral measure on a finite torus Path integrals in finite volume require a bit of care in order to get the overall normalization correct – we mostly follow the method of =-=[77]-=-, deviating from the presentation there only in details particular to the application here. Define the measure – for the gauge group, the gauge field, and the B field – as in [77], in a local way. To ... |

22 | From Linear SUSY to Constrained Superfields,”
- Komargodski, Seiberg
- 2009
(Show Context)
Citation Context ...tion 35 References 47 2 1 Introduction Recently there has been much progress in understanding Fayet-Iliopoulos parameters in supergravity, generalizing work of e.g. Bagger-Witten [1], see for example =-=[2, 3, 4, 5, 6, 7, 8, 9]-=-. In particular, the recent paper [7] argued that in the special case of linearlyrealized group actions, Fayet-Iliopoulos parameters could be interpreted as charges for a U(1) gauge symmetry, and so a... |

21 | Orbifold quantum cohomology of weighted projective spaces
- Mann
(Show Context)
Citation Context |

20 | GLSM’s for gerbes (and other toric stacks
- Pantev, Sharpe
(Show Context)
Citation Context ...Iliopoulos quantization when the moduli space is defined by two-dimensional sigma models with a restriction on allowed instantons. Such two-dimensional theories have been discussed previously in e.g. =-=[10, 11, 12, 13, 14, 15, 16]-=-, and are the same as sigma models on gerbes, special kinds of stacks. Schematically, smooth stacks are “manifolds paired with automorphisms.” Stacks admit metrics, spinors, and all the other structur... |

20 |
Quantum symmetries of string vacua
- Vafa
- 1989
(Show Context)
Citation Context ... of the moduli space to be physically relevant. On the ten-dimensional heterotic string worldsheet, this proposed Z2 gerbe structure on the CFT moduli space manifests itself as the quantum symmetry11 =-=[51]-=- associated with the left-moving GSO analogue that defines the Spin(32)/Z2 string in its RNS presentation. (The center of Spin(32) is Z2×Z2, and the GSO analogue itself is responsible for the Z2 quoti... |

19 |
Supersymmetric solitons
- Shifman, Yung
- 2009
(Show Context)
Citation Context ...sets, and here we seem to have found the same structure in homotopy of a moduli stack. Unfortunately, further analysis does not seem to bear out this perspective. One seeming counterexample arises in =-=[62]-=-[section 4.2]. That reference also describes Zn cosmic strings, though in that case, the adjoints act primarily as spectators, and the cosmic string solution naturally involves winding of vevs of mass... |

15 |
private communication
- Pantev
(Show Context)
Citation Context ...ess (see e.g. [41] for a more detailed discussion). One might ask if there is an alternative description as some Z(G)×Z(LG) gerbe over another space, giving a duality-invariant stack, but we are told =-=[42]-=- such a construction does not exist. Let us next consider some examples of gerbe structures appearing in the field theories discussed in [43, 44, 45, 46]. These papers discuss examples in which an N =... |

15 |
The Etiology Of Sigma Model Anomalies
- Moore, Nelson
- 1985
(Show Context)
Citation Context ...rt for smooth manifolds. In the text we listed a number of interesting possible followups. Another direction that would be interesting to pursue is sigma model anomalies, in the sense of Moore-Nelson =-=[71, 72, 73]-=-, in cases where the target space is a gerbe or other stack. Yet another direction concerns deformation issues. Briefly, stacks and underlying spaces do not always admit the same deformations. To illu... |

14 | On the Cn/Zm fractional brane - Karp - 2009 |

13 | Comments on the Fayet-Iliopoulos term in field theory and supergravity
- Komargodski, Seiberg
(Show Context)
Citation Context ... act ineffectively on right-movers but effectively on left-movers. Examples can also be constructed in (0,2) GLSM’s, such as the (anomaly-free, fractional) bundle 0 −→ E −→ O(1)⊕9 −→ O(9) −→ 0 over P3=-=[2,2,2,4]-=-[10], a Z2 gerbe over P 3 [1,1,1,2][5]. Other two-dimensional examples have been constructed by dimensional reduction of twisted four-dimensional N = 2 theories, as in [32]. These examples all seem to... |

13 |
Heterotic string theory I: the free heterotic string,” Nucl. Phys. B256
- Gross, Harvey, et al.
- 1985
(Show Context)
Citation Context ...resent case, the Spin(32)/Z2 heterotic string has at its first massive level states transforming in the spinor representation of Spin(32)/Z2, which is not invariant under the Z2 ([48][section 6.3.1], =-=[49]-=-[section 2.3]), exactly as needed for a gerbe description of the moduli space to be physically relevant. On the ten-dimensional heterotic string worldsheet, this proposed Z2 gerbe structure on the CFT... |

12 | Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity.
- Komargodski, Seiberg
- 2010
(Show Context)
Citation Context ...tion 35 References 47 2 1 Introduction Recently there has been much progress in understanding Fayet-Iliopoulos parameters in supergravity, generalizing work of e.g. Bagger-Witten [1], see for example =-=[2, 3, 4, 5, 6, 7, 8, 9]-=-. In particular, the recent paper [7] argued that in the special case of linearlyrealized group actions, Fayet-Iliopoulos parameters could be interpreted as charges for a U(1) gauge symmetry, and so a... |

12 |
String compactifications on Calabi-Yau stacks,” Nucl. Phys. B733
- Pantev, Sharpe
- 2006
(Show Context)
Citation Context ... 10A stack with non-finite stabilizers is known as an Artin stack. The geometric interpretation of Artin stacks is somewhat more complicated than that of Deligne-Mumford stacks, which the analysis of =-=[10, 11, 12, 13, 14, 15, 19, 20, 21, 16]-=- focused on. In this paper we also almost exclusively focus on Deligne-Mumford stacks. 13 gauge group. If we return again to Yang-Mills theories with adjoint matter, this means we consider the gerbe s... |

11 | Symmetries and Strings in Field Theory and Gravity - Banks, Seiberg - 2011 |

11 | Cluster decomposition, T-duality, and gerby CFT’s
- Hellerman, Henriques, et al.
(Show Context)
Citation Context ... Since the Z2 center acts trivially, one might naively assume that the [T 6/D4] orbifold would be physically equivalent to a [T 6/Z2×Z2] orbifold. Instead, one computes that at one-loop, for example, =-=[14]-=-[section 5.2] Z ( [T 6/D4] ) = Z ( [T 6/Z2 × Z2] ∐ [T 6/Z2 × Z2]d.t. ) , where the subscript indicates the presence of discrete torsion in one of the two factors. We therefore see explicitly that, in ... |

11 | On the geometry of quiver gauge theories (Stacking exceptional collections
- Herzog, Karp
- 2006
(Show Context)
Citation Context ... the sum over worldsheet instantons is restricted to a subset of all instantons is the same as 4 a string on a gerbe, a special kind of stack, as is discussed in the physics literature in for example =-=[10, 11, 12, 13, 14, 15, 16, 17, 18]-=- and reviewed in conference proceedings including [19, 20, 21]. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] f... |

11 |
private communication
- Knutson
(Show Context)
Citation Context ...ture, the matter would all have to be invariant under the center of the low-energy effective gauge group (in this case, E6, with center Z3). Neither 27’s nor 27’s are invariant under the center of E6 =-=[57]-=-, hence we do not expect to get a gerbe structure on the CFT moduli space, since there is not a gerbe structure on the field theory moduli space. More generally, it is worth emphasizing that many modu... |

10 |
Algebraic stacks, Proc
- Gómez
(Show Context)
Citation Context ...literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] for a few representative examples.) Briefly, a stack is a manifold “paired with automorphisms.” (See e.g. =-=[26, 27, 28]-=- for a more technical definition.) At the same level of brevity, a gerbe is a stack in which one has the same automorphisms everywhere. Mathematically, a gerbe can be thought of locally as covered by ... |

10 |
String Calculation Of Fayet-Iliopoulos D-Terms
- Atick, Dixon, et al.
- 1987
(Show Context)
Citation Context ...efold with the standard embedding. The low-energy gauge group is12 Spin(26)× U(1) Z4 . The U(1) factor is typically anomalous and Higgsed via a four-dimensional version of the Green-Schwarz mechanism =-=[54, 55]-=-, closely related to a (field-dependent, hence not directly relevant to this paper) Fayet-Iliopoulos parameter. The remaining Z2 center of Spin(32)/Z2 descends to part of the center of the group above... |

9 |
Duality theorems of étale gerbes on orbifolds, preprint. arXiv:1004.1376
- Tang, Tseng
(Show Context)
Citation Context ...mposition conjecture. One of the applications of the result above is to Gromov-Witten theory, where it has been checked and applied to simplify computations of Gromov-Witten invariants of gerbes, see =-=[33, 34, 35, 36, 37, 38]-=-. Another application is to gauged linear sigma models [15], where it answers old questions about the meaning of the Landau-Ginzburg point in a GLSM for a complete intersection of quadrics, as well as... |

8 |
Landau-Ginzburg models, gerbes, and Kuznetsov’s homological projective duality
- Sharpe
- 2010
(Show Context)
Citation Context ... same as 4 a string on a gerbe, a special kind of stack, as is discussed in the physics literature in for example [10, 11, 12, 13, 14, 15, 16, 17, 18] and reviewed in conference proceedings including =-=[19, 20, 21]-=-. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] for a few representative examples.) Briefly, a stack is a manif... |

8 | Gromov-Witten theory of etale gerbes, i: root gerbes,” arXiv: 0907.2087
- Andreini, Jiang, et al.
(Show Context)
Citation Context ...mposition conjecture. One of the applications of the result above is to Gromov-Witten theory, where it has been checked and applied to simplify computations of Gromov-Witten invariants of gerbes, see =-=[33, 34, 35, 36, 37, 38]-=-. Another application is to gauged linear sigma models [15], where it answers old questions about the meaning of the Landau-Ginzburg point in a GLSM for a complete intersection of quadrics, as well as... |

8 |
Intriligator, Misleading anomaly matchings?, Phys
- Brodie, Cho, et al.
- 1998
(Show Context)
Citation Context ...as properties of light particles. It would also be interesting if gerbe structures could be used to help disentangle confusing potential Seiberg duals. Examples of such are discussed in, for example, =-=[74]-=-, and there is a gerbe structure on some of the moduli spaces of the field theories discussed there. Similarly, it would be interesting to understand the three-dimensional ‘mirrors’ [75] to theories w... |

7 | Holomorphic reduction of N = 2 gauge theories, Wilson-’t Hooft operators, and S-duality,” [arXiv: hep-th/0612119
- Kapustin
(Show Context)
Citation Context ...ure, that is not really the case in (2,2) theories, as one gets sums of existing theories. In (0,2) theories, on the other hand, the story seems to be somewhat more complex; an example is outlined in =-=[32]-=-[section 3.2], and a more complete description will appear in [16]. We can understand the decomposition conjecture schematically as follows. Consider a nonlinear sigma model on a space X , for simplic... |

7 | Gromov-Witten theory of product stacks
- Andreini, Jiang, et al.
(Show Context)
Citation Context ...mposition conjecture. One of the applications of the result above is to Gromov-Witten theory, where it has been checked and applied to simplify computations of Gromov-Witten invariants of gerbes, see =-=[33, 34, 35, 36, 37, 38]-=-. Another application is to gauged linear sigma models [15], where it answers old questions about the meaning of the Landau-Ginzburg point in a GLSM for a complete intersection of quadrics, as well as... |

7 | Mirror symmetry, Hitchin’s equations, and Langlands duality. The many facets of geometry
- Witten
- 2010
(Show Context)
Citation Context ...ion of the decomposition conjecture of [14] to the two-dimensional sigma model on the gerbe then quickly reproduces the multiple component structure worked out more painfully by [39], as discussed in =-=[14, 40]-=-. One lesson of the example from geometric Langlands above is that these formal gerbe structures on moduli spaces do have physical content – the disconnectedness of the target of the two-dimensional s... |

7 |
Langlands duality for Hitchin systems. Arxiv preprint math.AG/0604617
- Donagi, Pantev
- 2006
(Show Context)
Citation Context ...ic class in H2(X, π1(G)), and the components are indexed by the value of that characteristic class. The effect of Langlands duality is to exchange Z(G) gerbiness with π1( LG) disconnectness (see e.g. =-=[41]-=- for a more detailed discussion). One might ask if there is an alternative description as some Z(G)×Z(LG) gerbe over another space, giving a duality-invariant stack, but we are told [42] such a constr... |

7 |
phases, spinors and monopoles
- Strassler, “Duality
- 1998
(Show Context)
Citation Context ...r space, giving a duality-invariant stack, but we are told [42] such a construction does not exist. Let us next consider some examples of gerbe structures appearing in the field theories discussed in =-=[43, 44, 45, 46]-=-. These papers discuss examples in which an N = 1 supersymmetric gauge theory with a gerbe structure on its moduli space is (Seiberg-)dual to another N = 1 supersymmetric gauge theory which has monopo... |

6 |
Modifying the sum over topological sectors and constraints on supergravity
- Seiberg
(Show Context)
Citation Context ...tion 35 References 47 2 1 Introduction Recently there has been much progress in understanding Fayet-Iliopoulos parameters in supergravity, generalizing work of e.g. Bagger-Witten [1], see for example =-=[2, 3, 4, 5, 6, 7, 8, 9]-=-. In particular, the recent paper [7] argued that in the special case of linearlyrealized group actions, Fayet-Iliopoulos parameters could be interpreted as charges for a U(1) gauge symmetry, and so a... |

6 |
Derived categories and stacks in physics,” contribution to the proceedings of the ESI research conference on homological mirror symmetry
- Sharpe
- 2006
(Show Context)
Citation Context ... same as 4 a string on a gerbe, a special kind of stack, as is discussed in the physics literature in for example [10, 11, 12, 13, 14, 15, 16, 17, 18] and reviewed in conference proceedings including =-=[19, 20, 21]-=-. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] for a few representative examples.) Briefly, a stack is a manif... |

6 |
GLSM’s, gerbes, and Kuznetsov’s homological projective duality,” contribution to the proceedings of Quantum theory and symmetries 6, arXiv
- Sharpe
(Show Context)
Citation Context ... same as 4 a string on a gerbe, a special kind of stack, as is discussed in the physics literature in for example [10, 11, 12, 13, 14, 15, 16, 17, 18] and reviewed in conference proceedings including =-=[19, 20, 21]-=-. (There is also a significant mathematics literature on Gromov-Witten invariants of stacks and gerbes; see for example [22, 23, 24, 25] for a few representative examples.) Briefly, a stack is a manif... |

6 |
On degree zero elliptic orbifold Gromov-Witten invariants,” arXiv: 0912.3580
- Tseng
(Show Context)
Citation Context |

6 |
On Donaldson-Thomas invariants of threefold stacks and gerbes,” arXiv: 1001.0435
- Gholampour, Tseng
(Show Context)
Citation Context |

6 | On the geometry of Deligne-Mumford stacks
- Kresch
- 2009
(Show Context)
Citation Context ... are classified by the homotopy groups of the moduli space M : cosmic strings13 arise from π1(M), monopoles from π2(M), textures from π3(M). Homotopy groups can be defined for moduli stacks (see e.g. =-=[60]-=- and references therein), and in particular for moduli spaces with gerbe structures, and are not quite the same as the homotopy groups of the underlying spaces. In this section we will outline such ho... |

5 |
Notes on gauging noneffective group actions,” arXiv: hep-th/0502027
- Pantev, Sharpe
(Show Context)
Citation Context ...Iliopoulos quantization when the moduli space is defined by two-dimensional sigma models with a restriction on allowed instantons. Such two-dimensional theories have been discussed previously in e.g. =-=[10, 11, 12, 13, 14, 15, 16]-=-, and are the same as sigma models on gerbes, special kinds of stacks. Schematically, smooth stacks are “manifolds paired with automorphisms.” Stacks admit metrics, spinors, and all the other structur... |

5 |
On Gromov-Witten theory of root gerbes,” arXiv: 0812.4477
- Andreini, Jiang, et al.
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5 |
A comment on sigma model anomalies,” Phys. Lett. B152
- Manohar, Moore, et al.
- 1985
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Citation Context ...rt for smooth manifolds. In the text we listed a number of interesting possible followups. Another direction that would be interesting to pursue is sigma model anomalies, in the sense of Moore-Nelson =-=[71, 72, 73]-=-, in cases where the target space is a gerbe or other stack. Yet another direction concerns deformation issues. Briefly, stacks and underlying spaces do not always admit the same deformations. To illu... |

4 | Global symmetries and D-terms in supersymmetric field theories
- Dumitrescu, Komargodski, et al.
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4 | On phases of gauge theories and the role of non-BPS solitons in field theory,” arXiv: hep-th/9808073
- Strassler
(Show Context)
Citation Context ...r space, giving a duality-invariant stack, but we are told [42] such a construction does not exist. Let us next consider some examples of gerbe structures appearing in the field theories discussed in =-=[43, 44, 45, 46]-=-. These papers discuss examples in which an N = 1 supersymmetric gauge theory with a gerbe structure on its moduli space is (Seiberg-)dual to another N = 1 supersymmetric gauge theory which has monopo... |

4 |
D-branes and K theory,” JHEP 9812
- Witten
- 1998
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Citation Context ...44, 45, 46] in the previous subsection, there exists a particle-type topological defect in type I string theory, arising from an element of π8(SO(32)), which transforms as a spinor of the Lie algebra =-=[52]-=-, the same property as a massive perturbative state in the dual heterotic Spin(32)/Z2 theory. Along special loci this gerbe structure can be enhanced, as expected on general grounds from our discussio... |

3 |
D-branes, orbifolds, and Ext groups,” Nucl. Phys. B673
- Katz, Pantev, et al.
- 2003
(Show Context)
Citation Context ...Iliopoulos quantization when the moduli space is defined by two-dimensional sigma models with a restriction on allowed instantons. Such two-dimensional theories have been discussed previously in e.g. =-=[10, 11, 12, 13, 14, 15, 16]-=-, and are the same as sigma models on gerbes, special kinds of stacks. Schematically, smooth stacks are “manifolds paired with automorphisms.” Stacks admit metrics, spinors, and all the other structur... |

3 |
A chiral SU(n) gauge theory and its nonchiral
- Pouliot, Strassler
- 1996
(Show Context)
Citation Context ...r space, giving a duality-invariant stack, but we are told [42] such a construction does not exist. Let us next consider some examples of gerbe structures appearing in the field theories discussed in =-=[43, 44, 45, 46]-=-. These papers discuss examples in which an N = 1 supersymmetric gauge theory with a gerbe structure on its moduli space is (Seiberg-)dual to another N = 1 supersymmetric gauge theory which has monopo... |

3 |
Notes on N = 2 sigma models
- Distler
- 1992
(Show Context)
Citation Context ...e SCFT moduli space admits a gerbe structure, and the Kähler form arises from a fractional line bundle, then there is an interesting structure on the worldsheet operators over SCFT moduli space (see =-=[70]-=- for a discussion for ordinary moduli spaces). Specifically, as we walk around the SCFT moduli space, some of the worldsheet operators (including the spectral flow operator) acquire phases from the (f... |

2 |
Quantization of Fayet-Iliopoulos Parameters in Supergravity,” Phys
- Distler, Sharpe
- 2011
(Show Context)
Citation Context ...cases with gerby moduli spaces. 23 6 Consistency conditions on classical supergravity In this section we will discuss consistency conditions on classical supergravities. We begin by reviewing results =-=[1, 7, 8]-=- for the case that the moduli space is a smooth manifold, and then we generalize to smooth Deligne-Mumford stacks, focusing on gerbes over manifolds. 6.1 Review of standard supergravity case First, le... |

2 |
Anomalies in nonlinear sigma models,” Phys
- Moore, Nelson
- 1984
(Show Context)
Citation Context ...rt for smooth manifolds. In the text we listed a number of interesting possible followups. Another direction that would be interesting to pursue is sigma model anomalies, in the sense of Moore-Nelson =-=[71, 72, 73]-=-, in cases where the target space is a gerbe or other stack. Yet another direction concerns deformation issues. Briefly, stacks and underlying spaces do not always admit the same deformations. To illu... |

1 |
Conserved currents and Fayet-Iliopoulos terms in supergravity,” arXiv
- Butter
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1 |
Heterotic strings on gerbes
- Pantev, Sharpe
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1 |
F-theory with quantized fluxes,” arXiv: hep-th/9805056
- Bershadsky, Pantev, et al.
(Show Context)
Citation Context ... us with the maximal commutant shown. We would like to thank A. Knutson for a useful discussion of this issue. 19 Specifically, it has been observed [42] that the multisection structures appearing in =-=[56]-=- in the F theory duals of heterotic CHL strings have an alternative interpretation in terms of elliptic fibrations over Z2 gerbes. Part of the point is that a heterotic compactification on an elliptic... |

1 | Donaldson invariants of CP1 × CP1 and mock theta functions,” arXiv
- Malmendier
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Citation Context .... It would also be interesting to understand if the ideas in this paper could be applied to understand the distinctions between SU(2) and SO(3) Donaldson and related mathematical invariants, see e.g. =-=[76]-=- and references therein. 33 8 Acknowledgements Some of the ideas in this paper have germinated over the last decade and been discussed with numerous people, more than we can list here. In particular, ... |