### Citations

376 | Mirror manifolds and topological field theory
- Witten
- 1998
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Citation Context ...opological twists When the superpotential vanishes (and, for ordinary chiral multiplets, X = 0), there are no curvature couplings, and the theories admit the same topological twists discussed in e.g. =-=[37]-=-. When the superpotential is nonzero, this story is more complicated. Sometimes those curvature couplings are incompatible with the topological twist (which can sometimes be 10 alleviated by twisting ... |

363 | Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” 0712.2824
- Pestun
(Show Context)
Citation Context ... be cohomologically trivial. Furthermore, supersymmetric localization techniques have been applied to theories of this form to obtain quantum mechanically exact results such as the partition function =-=[15, 16, 17, 18, 19, 20, 21]-=-. Recently these methods were applied to two-dimensional gauged linear sigma models (GLSMs) to derive exact expressions for partition functions [20, 21], which has quickly led to some interesting new ... |

249 |
Exact Results for Wilson Loops
- Kapustin, Willett, et al.
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Citation Context ... be cohomologically trivial. Furthermore, supersymmetric localization techniques have been applied to theories of this form to obtain quantum mechanically exact results such as the partition function =-=[15, 16, 17, 18, 19, 20, 21]-=-. Recently these methods were applied to two-dimensional gauged linear sigma models (GLSMs) to derive exact expressions for partition functions [20, 21], which has quickly led to some interesting new ... |

196 | The Exact Superconformal R-Symmetry Extremizes Z,” arXiv:1012.3210 [hep-th
- Jafferis
(Show Context)
Citation Context ... be cohomologically trivial. Furthermore, supersymmetric localization techniques have been applied to theories of this form to obtain quantum mechanically exact results such as the partition function =-=[15, 16, 17, 18, 19, 20, 21]-=-. Recently these methods were applied to two-dimensional gauged linear sigma models (GLSMs) to derive exact expressions for partition functions [20, 21], which has quickly led to some interesting new ... |

84 | Supersymmetry and supergravity”, second edition - Wess, Bagger - 1992 |

59 |
et al., Mirror symmetry
- Hori, Katz, et al.
- 2003
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Citation Context ...uperfields without curvature couplings As twisted chiral multiplets are discussed less commonly than ordinary chiral multiplets, it will be useful to review a few of their basic properties. (See also =-=[41]-=-[section 12.2] for another comparison of ordinary and twisted chiral multiplets.) Given twisted chiral multiplets of the form (ρi, χ̄i+, χ i − ), where the ρ are bosons, the Lagrangian for a theory co... |

50 |
Superspace formulation of new nonlinear sigma models, Nucl. Phys. B238
- Gates, James
- 1984
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Citation Context ...en r →∞, as one would expect. 1 As an aside, terms closely analogous to the curvature-dependent terms in the Lagrangian above have been discussed in two-dimensional theories in a different context in =-=[29]-=-. 4 There are two conditions on the data above. First, the Kähler potential is invariant under the isometry defined by the holomorphic Killing vector X , which means that on each coordinate patch, LX... |

38 |
personal communication
- Bryant
- 1997
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Citation Context ..., the f ’s are constrained to obey∑ i X i∂if(φ) = 0. (7) On a Kähler manifold with a holomorphic isometry X , for data on a good open cover, one can always choose K’s, f ’s to obey these constraints =-=[30]-=-. The second condition says that the superpotential W is homogeneous of degree 2 under the vector-like U(1)R symmetry, meaning 2W − iX iWi = 0 (8) (up to an additive constant). In particular, if X = 0... |

35 |
Exact Kahler Potential from Gauge Theory
- Gomis, Lee
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Citation Context ...kly led to some interesting new computational methods and results for Gromov-Witten invariants [22, 23, 24] and the Seiberg-Witten Kähler potential [25], as well as other insights into older results =-=[26]-=-. As part of that work, the papers [20, 21] worked out curvature couplings in two-dimensional linear sigma models whose target spaces are vector spaces. In this paper, we return to [20, 21] to re-exam... |

33 | Rigid supersymmetric theories in curved superspace - Festuccia, Seiberg - 2011 |

28 |
Partition functions of
- Benini, Cremonesi
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25 | Exploring Curved Superspace
- Dumitrescu, Festuccia, et al.
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Citation Context ...1 Introduction In recent years, curvature couplings in rigidly supersymmetric nonlinear sigma models on nontrivial spacetime manifolds of various dimensions have been discussed by several groups, see =-=[1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 14]-=- and references contained therein. Often, supersymmetry on the nontrivial spacetime manifold will constrain the target space in some fashion, by e.g. requiring the Kähler form on the target space to ... |

24 | Sums over topological sectors and quantization of FayetIliopoulos parameters
- Hellerman, Sharpe
(Show Context)
Citation Context ...tiplet, their components mix holomorphic and antiholomorphic target space indices: χ = ( χi − χı̄+ ) , χ̄ = ( χ̄ı̄ − χ̄i+ ) (11) 2 We would like to thank I. Melnikov for making this observation. 3See =-=[32, 33, 34, 35]-=- for a recent discussion of the Fayet-Iliopoulos parameter in supergravity, and how old obstruction issues summarized in e.g. [36] can be circumvented. 4 We do not attempt to consider H-flux backgroun... |

21 | Notes on certain other (0,2) correlation functions
- Sharpe
(Show Context)
Citation Context ...undle TM to T ∗M on the right-movers, the effect would be to convert the twisted chiral multiplets back into chiral multiplets. This is a special case of a duality in (0,2) theories discussed in e.g. =-=[42]-=-. Now, let us specialize to the caseW = 0, in which case there are no curvature couplings on any worldsheet, and consider topological twists. It is straightforward to topologically twist the theory of... |

14 |
Supersymmetric Gauge Theories on the Five-Sphere
- Hosomichi, Seong, et al.
- 2012
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12 | Rigidly supersymmetric gauge theories on curved superspace
- Jia, Sharpe
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Citation Context ...1 Introduction In recent years, curvature couplings in rigidly supersymmetric nonlinear sigma models on nontrivial spacetime manifolds of various dimensions have been discussed by several groups, see =-=[1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 14]-=- and references contained therein. Often, supersymmetry on the nontrivial spacetime manifold will constrain the target space in some fashion, by e.g. requiring the Kähler form on the target space to ... |

11 |
Supersymmetry on curved spaces and holography
- Klare, Tomasiello, et al.
(Show Context)
Citation Context ...1 Introduction In recent years, curvature couplings in rigidly supersymmetric nonlinear sigma models on nontrivial spacetime manifolds of various dimensions have been discussed by several groups, see =-=[1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 14]-=- and references contained therein. Often, supersymmetry on the nontrivial spacetime manifold will constrain the target space in some fashion, by e.g. requiring the Kähler form on the target space to ... |

11 |
Killing spinors on spheres and hyperbolic manifolds,” J.Math.Phys
- Fujii, Yamagishi
- 1986
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Citation Context ...re Qα and Q̄α are the supersymmetry generators, Jm are the generators of the SU(2) isometry of S2, and R is the generator of the U(1)R symmetry. The space of Killing spinors on S2 is four-dimensional =-=[28]-=-; a useful basis of this space consists of two Killing spinors called positive Killing spinors and two Killing spinors called negative Killing spinors [20]. Let’s denote the positive Killing spinors a... |

11 | Symmetries and strings in field theory and gravity,” arXiv
- Banks, Seiberg
(Show Context)
Citation Context ...tiplet, their components mix holomorphic and antiholomorphic target space indices: χ = ( χi − χı̄+ ) , χ̄ = ( χ̄ı̄ − χ̄i+ ) (11) 2 We would like to thank I. Melnikov for making this observation. 3See =-=[32, 33, 34, 35]-=- for a recent discussion of the Fayet-Iliopoulos parameter in supergravity, and how old obstruction issues summarized in e.g. [36] can be circumvented. 4 We do not attempt to consider H-flux backgroun... |

10 |
Supersymmetry in Lorentzian curved spaces and holography,” arXiv:1207.2181 [hep-th
- Cassani, Klare, et al.
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10 | Predictions for Gromov-Witten invariants of noncommutative resolutions,” arXiv
- Sharpe
(Show Context)
Citation Context ... linear sigma models (GLSMs) to derive exact expressions for partition functions [20, 21], which has quickly led to some interesting new computational methods and results for Gromov-Witten invariants =-=[22, 23, 24]-=- and the Seiberg-Witten Kähler potential [25], as well as other insights into older results [26]. As part of that work, the papers [20, 21] worked out curvature couplings in two-dimensional linear si... |

10 |
On the Inconsistency of Fayet-Iliopoulos Terms
- Dienes, Thomas
(Show Context)
Citation Context ...ke to thank I. Melnikov for making this observation. 3See [32, 33, 34, 35] for a recent discussion of the Fayet-Iliopoulos parameter in supergravity, and how old obstruction issues summarized in e.g. =-=[36]-=- can be circumvented. 4 We do not attempt to consider H-flux backgrounds in this paper. 7 In this section, we will work with Killing spinors ζ , ζ̄ obeying ∇mζ = i 2r γmζ, ∇mζ̄ = − i 2r γmζ̄ , (12) a ... |

10 | A-twisted Landau-Ginzburg models
- Guffin, Sharpe
(Show Context)
Citation Context ...tential is nonzero, this story is more complicated. Sometimes those curvature couplings are incompatible with the topological twist (which can sometimes be 10 alleviated by twisting bosons as in e.g. =-=[38, 39]-=-). However, a more fundamental problem is that even if one can consistently twist the theory, the curvature terms induced by the superpotential break the BRST symmetry, in the sense that the action is... |

10 | A-twisted heterotic Landau-Ginzburg models
- Guffin, Sharpe
(Show Context)
Citation Context ...tential is nonzero, this story is more complicated. Sometimes those curvature couplings are incompatible with the topological twist (which can sometimes be 10 alleviated by twisting bosons as in e.g. =-=[38, 39]-=-). However, a more fundamental problem is that even if one can consistently twist the theory, the curvature terms induced by the superpotential break the BRST symmetry, in the sense that the action is... |

9 | New methods for characterizing phases of 2d supersymmetric gauge theories,” arXiv
- Halverson, Kumar, et al.
(Show Context)
Citation Context ... linear sigma models (GLSMs) to derive exact expressions for partition functions [20, 21], which has quickly led to some interesting new computational methods and results for Gromov-Witten invariants =-=[22, 23, 24]-=- and the Seiberg-Witten Kähler potential [25], as well as other insights into older results [26]. As part of that work, the papers [20, 21] worked out curvature couplings in two-dimensional linear si... |

9 | The Seiberg-Witten Kähler potential as a two-sphere partition function
- Park, Song
(Show Context)
Citation Context ...ns for partition functions [20, 21], which has quickly led to some interesting new computational methods and results for Gromov-Witten invariants [22, 23, 24] and the Seiberg-Witten Kähler potential =-=[25]-=-, as well as other insights into older results [26]. As part of that work, the papers [20, 21] worked out curvature couplings in two-dimensional linear sigma models whose target spaces are vector spac... |

7 | Two-Sphere Partition Functions and GromovWitten Invariants”.
- Jockers
- 2014
(Show Context)
Citation Context ... linear sigma models (GLSMs) to derive exact expressions for partition functions [20, 21], which has quickly led to some interesting new computational methods and results for Gromov-Witten invariants =-=[22, 23, 24]-=- and the Seiberg-Witten Kähler potential [25], as well as other insights into older results [26]. As part of that work, the papers [20, 21] worked out curvature couplings in two-dimensional linear si... |

6 | Rigid supersymmetric backgrounds of minimal off-shell supergravity
- Liu, Zayas, et al.
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6 | Supersymmetric field theories on three-manifolds
- Closset, Dumitrescu, et al.
- 2013
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6 |
Supersymmetry on three-dimensional Lorentzian curved spaces and black hole holography
- Hristov, Tomasiello, et al.
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6 | Exact results in d = 2 supersymmetric gauge theories,” 2012. Talk given at the conference
- Gomis
(Show Context)
Citation Context ...2, 2) chiral multiplet in two dimensions contains components (φi, φ̄ı̄, ψi, ψ̄ ı̄, F i, F̄ ı̄). The chiral fields φi, φ̄ı̄ parametrize the target space M , which is a Kähler manifold. As observed in =-=[20, 21]-=-, the U(1)R charges of the chiral fields φ i enter the definition of the Lagrangian of the linear sigma models on S2. To construct nonlinear sigma models on a worldsheet S2, one needs to use the holom... |

6 | Elliptic genera of Landau-Ginzburg models over nontrivial spaces
- Ando, Sharpe
(Show Context)
Citation Context ...e A-twisted Landau-Ginzburg models realized Mathai-Quillen classes which gave a mathematical understanding of the behavior of renormalization group flow, as a type of Thom class phenomenon. (See also =-=[40]-=- for closely analogous behaviors in elliptic genera.) It would be interesting to see if something analogous arises in localization computations. 11 6 Acknowledgements We thank Robert Bryant, Josh Lapa... |

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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5 | Global supersymmetry on curved spaces in various dimensions
- Kehagias, Russo
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5 |
Rigid 6D supersymmetry and localization
- Samtleben, Sezgin, et al.
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4 | Quantization of Fayet-Iliopoulos parameters
- Distler, Sharpe
(Show Context)
Citation Context ...tiplet, their components mix holomorphic and antiholomorphic target space indices: χ = ( χi − χı̄+ ) , χ̄ = ( χ̄ı̄ − χ̄i+ ) (11) 2 We would like to thank I. Melnikov for making this observation. 3See =-=[32, 33, 34, 35]-=- for a recent discussion of the Fayet-Iliopoulos parameter in supergravity, and how old obstruction issues summarized in e.g. [36] can be circumvented. 4 We do not attempt to consider H-flux backgroun... |

3 |
Rigid supersymmetric theories in 4d Riemannian space
- Samtleben, Tsimpis
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2 | N=2 supersymmetric Calabi-Yau hypersurface sigma-models on curved twodimensions, Phys
- Nishino
- 1995
(Show Context)
Citation Context ...del in [20, 21] can also be obtained by applying a decoupling gravity procedure analogous to the one in [1, 2] to the coupled theory of (2,2) gauged linear sigma model and (1,1) supergravity model in =-=[31]-=-. From the supersymmetry transformations above, we can get some insight into the constraint on W . Specifically, note that with the Killing spinor condition, the supersymmetry variation of the auxilia... |

1 |
Modifying the sum over topologicalsectors and constraints on supergravity
- Seiberg
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