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## Rigidly supersymmetric gauge theories on curved superspace (2012)

Venue: | JHEP |

Citations: | 12 - 2 self |

### Citations

289 | Electric-magnetic duality and the geometric Langlands program
- Kapustin, Witten
(Show Context)
Citation Context ...s (see for example [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] for a sample). Such theories have also been discussed implicitly in a number of other places in the physics literature (see for example =-=[50, 51, 52, 53, 54, 55, 56]-=-). 6 Conclusions and outlook Supersymmetric nonlinear sigma models and gauge theories on curved spacetime, as we have seen in this paper, have a lot of interesting properties that are absent in the us... |

215 |
A new cohomology theory for orbifold
- Chen, Ruan
(Show Context)
Citation Context ...with restrictions on nonperturbative sectors (sigma models on gerbes) in both the physics (see [4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]) and especially the math communities (see for example =-=[39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]-=- for a sample). Such theories have also been discussed implicitly in a number of other places in the physics literature (see for example [50, 51, 52, 53, 54, 55, 56]). 6 Conclusions and outlook Supers... |

148 | Conformal field theory correlators from classical scalar field theory
- Muck, Viswanathan
- 1998
(Show Context)
Citation Context ...bundles in an appendix. In passing, since one of the spaces we study will be AdS4, we should mention that, just as in previous papers [1, 2], we shall ignore the role of boundary conditions. See e.g. =-=[10, 11, 12, 13]-=- for an overview of boundary conditions in AdS4, and e.g. [14, 15, 16] for information on how such boundary conditions can restrict chiral matter representations. 2 Review of rigidly susy sigma models... |

127 | Gromov-Witten theory of Deligne-Mumford stacks
- Abramovich, Graber, et al.
(Show Context)
Citation Context ...with restrictions on nonperturbative sectors (sigma models on gerbes) in both the physics (see [4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]) and especially the math communities (see for example =-=[39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]-=- for a sample). Such theories have also been discussed implicitly in a number of other places in the physics literature (see for example [50, 51, 52, 53, 54, 55, 56]). 6 Conclusions and outlook Supers... |

84 |
Supersymmetry and supergravity”, second edition
- Wess, Bagger
- 1992
(Show Context)
Citation Context ...e resulting Lagrangian invariant. Let us review the approach of [2], as we shall apply it to gauge theories in the next 4 section. We start with the N = 1 chiral supergravity Lagrangian in superspace =-=[17]-=-: L = 1 κ2 ∫ d2Θ2E [ 3 8 (D̄D̄ − 8R) exp(−κ 2 3 K(Φi, Φ̄ı̄)) + κ2W (Φi) ] + h.c. (1) Then we remove the effect of gravity. First, we need to expand in κ2, then only keep the terms that are independent... |

60 |
Dynamics in nonglobally hyperbolic static space-times. 3. Anti-de Sitter space-time, Class.Quant.Grav
- Ishibashi, Wald
(Show Context)
Citation Context ...bundles in an appendix. In passing, since one of the spaces we study will be AdS4, we should mention that, just as in previous papers [1, 2], we shall ignore the role of boundary conditions. See e.g. =-=[10, 11, 12, 13]-=- for an overview of boundary conditions in AdS4, and e.g. [14, 15, 16] for information on how such boundary conditions can restrict chiral matter representations. 2 Review of rigidly susy sigma models... |

55 | The quantum orbifold cohomology of weighted projective spaces
- Coates, Corti, et al.
(Show Context)
Citation Context ...with restrictions on nonperturbative sectors (sigma models on gerbes) in both the physics (see [4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]) and especially the math communities (see for example =-=[39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]-=- for a sample). Such theories have also been discussed implicitly in a number of other places in the physics literature (see for example [50, 51, 52, 53, 54, 55, 56]). 6 Conclusions and outlook Supers... |

44 |
Boundary Conditions and New Dualities: Vector Fields
- Marolf, Ross
(Show Context)
Citation Context ...bundles in an appendix. In passing, since one of the spaces we study will be AdS4, we should mention that, just as in previous papers [1, 2], we shall ignore the role of boundary conditions. See e.g. =-=[10, 11, 12, 13]-=- for an overview of boundary conditions in AdS4, and e.g. [14, 15, 16] for information on how such boundary conditions can restrict chiral matter representations. 2 Review of rigidly susy sigma models... |

38 |
personal communication
- Bryant
- 1997
(Show Context)
Citation Context ...constant M , M̄ , 2. M = M̄ = 0, bµ a covariantly-constant vector. In the first case, if we Wick rotate to Euclidean space, it can be argued from the existence of spinors ζ in the gravitino variation =-=[19]-=- that the spacetime metric either has constant sectional curvature, or is Ricci-flat and self-dual or anti-self-dual. To see this, note in this case we have Killing spinor equations ∇µζα = i 6 M(ǫσµζ̄... |

33 | Rigid supersymmetric theories in curved superspace
- Festuccia, Seiberg
- 2011
(Show Context)
Citation Context ...ic nonlinear sigma model from supergravtiy. For example, we can decouple gravity in the weak coupling limit to get supersymmetric nonlinear sigma model on AdS4 [1]. On the other hand, it was noted in =-=[2]-=- that the auxiliary fields bµ and M from the N = 1 supergravity multiplet could be used to determine the geometry of spacetime, therefore generating two classes of spacetime geometries. The idea is to... |

29 |
Quantization of Newton’s constant in certain supergravity thoeries
- Witten, Bagger
- 1982
(Show Context)
Citation Context ...idly supersymmetric theories, which guarantees that the Kähler form on the quotient space is exact. Just as in N = 1 supergravity in four dimensions, the superpotential is a section of a line bundle =-=[7]-=-, we interpret the superpotential in these rigidly supersymmetric theories as a section of an affine bundle. Just as in N = 1 supergravity [4, 5], where the Fayet-Iliopoulos parameter was determined b... |

24 | Sums over topological sectors and quantization of FayetIliopoulos parameters
- Hellerman, Sharpe
(Show Context)
Citation Context ... trivially so. 20 5 Sigma models on stacks and restrictions on nonperturbative sectors Physically, in supergravity theories we often want to work with moduli spaces possessing finite group symmetries =-=[6, 5, 18]-=-. These are described mathematically by stacks [4, 5], certain generalizations of spaces. (In fact, mathematically most moduli ‘spaces’ are actually stacks, so to really make contact between the super... |

23 | Non-birational twisted derived equivalences in abelian GLSMs
- Caldararu, Distler, et al.
(Show Context)
Citation Context ..., rather than to particular quotients [X/G]. In two dimensions, there are now extensive checks that renormalization group flow does indeed identify different presentations of the same stack (see e.g. =-=[28, 29, 30, 31, 32]-=-), though in four dimensions there are suggestions [5] that the same program might not work. (As an extreme example, since the gauge kinetic term is not fixed, some references consider ChernSimons the... |

23 | Chiral duals of nonchiral SUSY gauge theories
- Pouliot
- 1995
(Show Context)
Citation Context ...s (see for example [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] for a sample). Such theories have also been discussed implicitly in a number of other places in the physics literature (see for example =-=[50, 51, 52, 53, 54, 55, 56]-=-). 6 Conclusions and outlook Supersymmetric nonlinear sigma models and gauge theories on curved spacetime, as we have seen in this paper, have a lot of interesting properties that are absent in the us... |

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 ..., rather than to particular quotients [X/G]. In two dimensions, there are now extensive checks that renormalization group flow does indeed identify different presentations of the same stack (see e.g. =-=[28, 29, 30, 31, 32]-=-), though in four dimensions there are suggestions [5] that the same program might not work. (As an extreme example, since the gauge kinetic term is not fixed, some references consider ChernSimons the... |

14 | On the Cn/Zm fractional branes
- Karp
(Show Context)
Citation Context ...rbative sectors are known as gerbes. Over the last decade, there has been extensive work on sigma models with restrictions on nonperturbative sectors (sigma models on gerbes) in both the physics (see =-=[4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]-=-) and especially the math communities (see for example [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] for a sample). Such theories have also been discussed implicitly in a number of other places in the ... |

13 | Comments on the Fayet-Iliopoulos term in field theory and supergravity
- Komargodski, Seiberg
(Show Context)
Citation Context ...upersymmetric theory to gravity. In such theories, 3 for e.g. couplings involving the Ferrara-Zumino multiplet, one also often sees that Kähler forms are exact and Fayet-Iliopoulos parameters vanish =-=[8, 9]-=-, just as we describe here for rigidly supersymmetric theories on e.g. AdS4. (As observed in [6], however, one should distinguish supergravities obtained by coupling a rigid theory to gravity, from mo... |

12 | Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity.
- Komargodski, Seiberg
- 2010
(Show Context)
Citation Context ...upersymmetric theory to gravity. In such theories, 3 for e.g. couplings involving the Ferrara-Zumino multiplet, one also often sees that Kähler forms are exact and Fayet-Iliopoulos parameters vanish =-=[8, 9]-=-, just as we describe here for rigidly supersymmetric theories on e.g. AdS4. (As observed in [6], however, one should distinguish supergravities obtained by coupling a rigid theory to gravity, from mo... |

12 |
String compactifications on Calabi-Yau stacks,” Nucl. Phys. B733
- Pantev, Sharpe
- 2006
(Show Context)
Citation Context ..., rather than to particular quotients [X/G]. In two dimensions, there are now extensive checks that renormalization group flow does indeed identify different presentations of the same stack (see e.g. =-=[28, 29, 30, 31, 32]-=-), though in four dimensions there are suggestions [5] that the same program might not work. (As an extreme example, since the gauge kinetic term is not fixed, some references consider ChernSimons the... |

11 | Symmetries and strings in field theory and gravity,” arXiv
- Banks, Seiberg
(Show Context)
Citation Context ... trivially so. 20 5 Sigma models on stacks and restrictions on nonperturbative sectors Physically, in supergravity theories we often want to work with moduli spaces possessing finite group symmetries =-=[6, 5, 18]-=-. These are described mathematically by stacks [4, 5], certain generalizations of spaces. (In fact, mathematically most moduli ‘spaces’ are actually stacks, so to really make contact between the super... |

11 | Cluster decomposition, T-duality, and gerby CFT’s
- Hellerman, Henriques, et al.
(Show Context)
Citation Context |

11 | On the geometry of quiver gauge theories: Stacking exceptional collections,’ arXiv: hep-th/0605177
- Herzog, Karp
(Show Context)
Citation Context ...rbative sectors are known as gerbes. Over the last decade, there has been extensive work on sigma models with restrictions on nonperturbative sectors (sigma models on gerbes) in both the physics (see =-=[4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]-=-) and especially the math communities (see for example [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] for a sample). Such theories have also been discussed implicitly in a number of other places in the ... |

10 | Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings
- Elvang, Freedman, et al.
(Show Context)
Citation Context ...uivariant structure. 19 In passing, we should note that the fact that in supergravity, Fayet-Iliopoulos parameters appear in anomalies, has been discussed elsewhere in the literature, see for example =-=[24, 25]-=- for an excellent description and overview. Now, let us return to the background principle and the discussion of anomalies. Much as in [1], in the gauged case the supergravity anomaly decomposes as PG... |

9 |
Duality theorems of étale gerbes on orbifolds,” arXiv
- Tang, Tseng
(Show Context)
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8 |
Landau-Ginzburg models, gerbes, and Kuznetsov’s homological projective duality,” to appear in the proceedings of Topology, C∗ algebras, string duality
- Sharpe
(Show Context)
Citation Context ...rbative sectors are known as gerbes. Over the last decade, there has been extensive work on sigma models with restrictions on nonperturbative sectors (sigma models on gerbes) in both the physics (see =-=[4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]-=-) and especially the math communities (see for example [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] for a sample). Such theories have also been discussed implicitly in a number of other places in the ... |

8 | Gromov-Witten theory of etale gerbes, i: root gerbes,” arXiv: 0907.2087
- Andreini, Jiang, et al.
(Show Context)
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7 |
Infrared Behavior at negative Curvature,” Nucl.Phys. B340
- Callan, Curtis, et al.
- 1990
(Show Context)
Citation Context ...be AdS4, we should mention that, just as in previous papers [1, 2], we shall ignore the role of boundary conditions. See e.g. [10, 11, 12, 13] for an overview of boundary conditions in AdS4, and e.g. =-=[14, 15, 16]-=- for information on how such boundary conditions can restrict chiral matter representations. 2 Review of rigidly susy sigma models on curved superspace There are several ways of deriving rigid supersy... |

7 | Affine line bundles and linearization
- Kraft, Kutzschebauch
- 1996
(Show Context)
Citation Context ...ne line bundle π : X ×A1 → X , which shows up in our discussion of 23 supersymmetric theories on AdS4. Let G be a group acting on X , then the G-action on the affine bundle π : X × A1 → X is given by =-=[23]-=- g(x, a) = (gx, λga+ µg(x)), ∀g ∈ G, x ∈ X, a ∈ A1, (62) where λ and µ are functions on G×X such that for any g, h ∈ G λgh = λg · λh, λe = 1, µgh(x) = λg · µh(x) + µg(hx), µe = 0. (63) Let s : X → X×A... |

7 | Gromov-Witten theory of product stacks,” arXiv: 0905.2258
- Andreini, Jiang, et al.
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7 | Mirror symmetry, Hitchin’s equations, and Langlands duality. The many facets of geometry
- Witten
- 2010
(Show Context)
Citation Context ...s (see for example [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] for a sample). Such theories have also been discussed implicitly in a number of other places in the physics literature (see for example =-=[50, 51, 52, 53, 54, 55, 56]-=-). 6 Conclusions and outlook Supersymmetric nonlinear sigma models and gauge theories on curved spacetime, as we have seen in this paper, have a lot of interesting properties that are absent in the us... |

7 |
Langlands duality for Hitchin systems. Arxiv preprint math.AG/0604617
- Donagi, Pantev
- 2006
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7 |
phases, spinors and monopoles
- Strassler, “Duality
- 1998
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6 |
Modifying the sum over topological sectors and constraints on supergravity,” arXiv
- Seiberg
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Citation Context ... of rigidly supersymmetric ungauged theories are constrained, we find analogous constraints in gauge theories. For example, just as the Fayet-Iliopoulos parameter is constrained in N = 1 supergravity =-=[4, 5, 6]-=-, we find a constraint on the Fayet-Iliopoulos parameter in rigidly supersymmetric theories, which guarantees that the Kähler form on the quotient space is exact. Just as in N = 1 supergravity in fou... |

6 |
Gauge Boson Mass Generation
- Rattazzi, Redi
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Citation Context ...be AdS4, we should mention that, just as in previous papers [1, 2], we shall ignore the role of boundary conditions. See e.g. [10, 11, 12, 13] for an overview of boundary conditions in AdS4, and e.g. =-=[14, 15, 16]-=- for information on how such boundary conditions can restrict chiral matter representations. 2 Review of rigidly susy sigma models on curved superspace There are several ways of deriving rigid supersy... |

6 |
Derived categories and stacks in physics,” contribution to the proceedings of the ESI research conference on homological mirror symmetry
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6 |
GLSM’s, gerbes, and Kuznetsov’s homological projective duality,” contribution to the proceedings of Quantum theory and symmetries 6, arXiv
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6 |
On degree zero elliptic orbifold Gromov-Witten invariants,” arXiv: 0912.3580
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6 |
On Donaldson-Thomas invariants of threefold stacks and gerbes,” arXiv: 1001.0435
- Gholampour, Tseng
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5 |
2 supersymmetric sigma models in AdS, Phys. Lett. B703 (2011) 620-626, arXiv: 1105.3111; The structure of N = 2 supersymmetric nonlinear sigma models
- Butter, Kuzenko, et al.
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Citation Context ...α by fα, for any holomorphic function fα on the patch. Only the combination of K and W is physically meaningful. One consequence of this phenomenon is that the target spaceX is necessarily noncompact =-=[1, 2, 3]-=-. Equation (17) not only requires the C̆ech cocycle (δf)αβγ = 0 on all triple overlaps, but also requires that the C̆ech cocycle be trivial (fαβ is a C̆ech coboundary), therefore the Kähler form of X... |

5 |
Notes on gauging noneffective group actions,” arXiv: hep-th/0502027
- Pantev, Sharpe
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5 |
On Gromov-Witten theory of root gerbes,” arXiv: 0812.4477
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4 | Quantization of Fayet-Iliopoulos parameters
- Distler, Sharpe
(Show Context)
Citation Context ... of rigidly supersymmetric ungauged theories are constrained, we find analogous constraints in gauge theories. For example, just as the Fayet-Iliopoulos parameter is constrained in N = 1 supergravity =-=[4, 5, 6]-=-, we find a constraint on the Fayet-Iliopoulos parameter in rigidly supersymmetric theories, which guarantees that the Kähler form on the quotient space is exact. Just as in N = 1 supergravity in fou... |

4 | On phases of gauge theories and the role of non-BPS solitons in field theory,” arXiv: hep-th/9808073
- Strassler
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3 | Kähler anomalies in supergravity and flux vacua,” hep-th/0509217
- Freedman, Körs
(Show Context)
Citation Context ...uivariant structure. 19 In passing, we should note that the fact that in supergravity, Fayet-Iliopoulos parameters appear in anomalies, has been discussed elsewhere in the literature, see for example =-=[24, 25]-=- for an excellent description and overview. Now, let us return to the background principle and the discussion of anomalies. Much as in [1], in the gauged case the supergravity anomaly decomposes as PG... |

3 | D-branes, orbifolds, and Ext groups,” Nucl. Phys. B673 - Katz, Pantev, et al. - 2003 |

3 | Gromov-Witten theory of banded gerbes over schemes,” arXiv
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3 |
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1 |
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1 |
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- Sen
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Citation Context ...new terms that are different from the familiar Minkowski spacetime model. Note these extra terms vanishes at the limit r →∞, so this theory reduces to the Minkowski case as expected. (See for example =-=[20, 21]-=- for further discussions of rigidly supersymmetric theories on this spacetime.) In this model the supersymmetry transformations are δζφ i = √ 2ζχi, δζχ i = √ 2F iζ + i √ 2σµζ̄∂µφ i, δζF i = √ 2ζ̄ α̇(i... |

1 |
Extended supersymmetry in the space-time R×S3,” Phys. Rev. D41
- Sen
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Citation Context ...new terms that are different from the familiar Minkowski spacetime model. Note these extra terms vanishes at the limit r →∞, so this theory reduces to the Minkowski case as expected. (See for example =-=[20, 21]-=- for further discussions of rigidly supersymmetric theories on this spacetime.) In this model the supersymmetry transformations are δζφ i = √ 2ζχi, δζχ i = √ 2F iζ + i √ 2σµζ̄∂µφ i, δζF i = √ 2ζ̄ α̇(i... |

1 |
Differential cohomology in a cohesive∞-topos,” Habilitation
- Schreiber
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(Show Context)
Citation Context ...at the same program might not work. (As an extreme example, since the gauge kinetic term is not fixed, some references consider ChernSimons theories to be examples of sigma models on stacks, see e.g. =-=[26]-=- though the inclination of the authors is to only consider Yang-Mills-type kinetic terms in such language.) In any event, as also observed in [5], even if stacks do not uniquely determine physics, nev... |