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## Extended Supersymmetry on Curved Spaces (2013)

Venue: | JHEP |

Citations: | 3 - 0 self |

### Citations

494 | Seiberg-Witten prepotential from instanton counting,” arXiv:hepth/0306211; N. Nekrasov and A. Okounkov, “Seiberg-Witten theory and random partitions,” arXiv:hep-th/0306238
- Nekrasov
(Show Context)
Citation Context ...1, 34] the authors analysed cases where at these points the geometry locally looks like the Ωdeformation of flat space and hence the instanton contribution is given by the Nekrasov partition function =-=[42]-=-. It would be interesting to study more general field theories on curved spaces and even cases with a non-degenerate Killing vector to see if in that case the localised partition function is exempt fr... |

389 | Liouville correlation functions from four-dimensional gauge theories
- Alday, Gaiotto, et al.
(Show Context)
Citation Context ... where the same theories were put on a squashed four-sphere, preserving some supersymmetry. The analysis allowed for a more detailed comparison with the 2-dimensional duals via the AGT correspondence =-=[39]-=-11. In this more general example background gauge and tensor fields take non-trivial values. In this section we want to discuss the geometrical constraints imposed by supersymmetry and determine gener... |

368 | Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” arXiv:0712.2824 [hep-th
- Pestun
(Show Context)
Citation Context ...e only way of preserving supersymmetry. For example, we can define a SCFT on any conformally flat curved space just by a conformal mapping from flat space. This is the case of the theories studied in =-=[1]-=-, for example. In between these two extreme situations there is a full spectrum of possibilities with different auxiliary fields that is investigated in this paper. In Lorentzian signature the conditi... |

265 | Seiberg-Witten theory and random partitions,” arXiv:hep-th/0306238 [hep-th
- Nekrasov, Okounkov
(Show Context)
Citation Context ... f tan ρ 2 ) − δx34c3 . The three parameters ci can be chosen as in [34] in order to have a regular solution on S4 which reduces at the North and South pole of the squashed sphere to the Ω-background =-=[41]-=- which plays an important role in reducing the computation of the partition function to the Nekrasov partition functions for instantons. The local form of this solution and the Ω-background are discus... |

251 | Exact Results for Wilson Loops - Kapustin, Willett, et al. |

200 | The Exact Superconformal R-Symmetry Extremizes Z - Jafferis |

111 |
Rigid Supersymmetric Theories
- Festuccia, Seiberg
(Show Context)
Citation Context ...f supersymmetric field theories on curved spaces has led to many interesting results in recent years, see for example [1–7]. The approach of coupling the theories to offshell supergravity, started in =-=[8]-=-, has led to a classification of supersymmetric backgrounds with Euclidean and Lorentzian signature for N = 1 theories in four dimensions [9–12] and for N = 2 theories in three dimensions [9, 13, 14].... |

48 | N=2 supersymmetric theories on squashed three-sphere - Imamura, Yokoyama |

38 |
Topological Quantum Field Theory,” Commun.Math.Phys
- Witten
- 1988
(Show Context)
Citation Context ...e partition function on some of these spaces, using supersymmetric localization techniques. A consistent supersymmetric definition of an N = 2 theory on any four-manifold has been first introduced in =-=[26]-=-. There, supersymmetry is preserved by twisting the SU(2) R-symmetry with one of the SU(2)’s of the Lorentz group SO(4). The background gauge field precisely cancels the spin connection for a spinor o... |

24 | Rigid supersymmetric theories - Samtleben, Tsimpis |

17 |
Gauged N=4 supergravities in five-dimensions and their magnetovac backgrounds, Nucl. Phys. B267
- Romans
- 1986
(Show Context)
Citation Context ...trivial) boundary, see e.g. [28]. This has been discussed recently in [9, 11] and seems to be true also for situations with more supersymmetry. In fact, expanding Roman’s N = 4 5d gauged supergravity =-=[29]-=- in an asymptotically AdS space, one finds [30] the conditions of 3 N = 2 superconformal supergravity in four dimensions [31,32] on the boundary. A similar analysis is true for general boundaries, whe... |

16 |
Four-dimensional conformal supergravity from AdS space
- Balasubramanian, Gimon, et al.
(Show Context)
Citation Context ...pective, as we can study a CFT via its holographic dual. Typically, minimal supergravity in asymptotically locally AdS spaces reduces to conformal supergravity on the (non-trivial) boundary, see e.g. =-=[28]-=-. This has been discussed recently in [9, 11] and seems to be true also for situations with more supersymmetry. In fact, expanding Roman’s N = 4 5d gauged supergravity [29] in an asymptotically AdS sp... |

15 | Supersymmetry on curved spaces and superconformal anomalies,” [arXiv:1307.6567 [hep-th - Cassani, Martelli |

13 | Superconformal quantum field theory in curved spacetime - Medeiros, Hollands |

13 |
Generalized structures of ten-dimensional supersymmetric solutions,”
- Tomasiello
- 2012
(Show Context)
Citation Context ...o by an appropriate Weyl rescaling. 5It is not excluded that more general solutions with non abelian gauge fields and a non-vanishing tensor exist but we will not discuss this case in our paper. 6See =-=[36]-=-, in particular Appendix A, for a nice review of the formalism. 7 We will find useful to work in the frame defined by en where the action of the gamma matrices on the spinors takes a very simple form.... |

12 | Rigidly Supersymmetric Gauge Theories on - Jia, Sharpe |

8 |
All solutions of the localization equations for N=2 quantum black hole entropy,” JHEP 1302
- Gupta, Murthy
- 2013
(Show Context)
Citation Context ...lds that preserve some of the extended supersymmetry. The Lorentzian case where part of the superconformal invariance is gauge fixed by compensators has already been analysed and completely solved in =-=[25]-=- for applications to black hole entropy1. Here we generalise the result to the full CKS equation and extend it to the Euclidean case. Although some of the supersymmetry constraints are differential, w... |

7 | Rigid supersymmetry, conformal coupling and twistor spinors, arXiv:1209.4043 - Medeiros |

6 | Symmetries of curved superspace - Kuzenko - 2013 |

6 |
Electric and magnetic charges in N=2 conformal supergravity theories
- Wit, Zalk
(Show Context)
Citation Context ... ∝ ǫ 2 + and zµ is null. We essentially fall in the N = 1 case that has been studied in [11]. In fact, by a 4An analysis of supersymmetry Lagrangians using conformal supergravity has also appeared in =-=[35]-=- where various explicit solutions have been discussed. 6 gauge transformation we can always set one of the spinors to zero. By further restricting the gauge fields to a suitable abelian subgroup and b... |

5 |
Pure spinor equations to lift gauged supergravity
- Rosa, Tomasiello
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Citation Context ... in our frame with constant spinors one has Pµx = 1 4 ωµ αβηxαβ Pµ0 = 1 2 ∂µ(B + iβ) (2.13) where ηxαβ projects on the self-dual part of the spin connection. A similar parametrisation has appeared in =-=[37]-=-. 2.3 Solving the supersymmetry conditions In this section we show that all manifolds with a timelike conformal Killing vector (CKV) admit a solution to the equations (2.4). Let us analyse the two con... |

3 | Localization on ThreeManifolds - Alday, Martelli, et al. |

3 | Killing spinors and SYM on curved spaces, JHEP 0011 - Blau - 2000 |

3 |
Topological quantum field theory and N=2 conformal supergravity, Phys.Lett. B212
- Karlhede, Rocek
- 1988
(Show Context)
Citation Context ...l overlap with section 2. 1 that we can define a consistent N = 2 theory on any Euclidean four manifold by a topological twist [26]. The twist was analysed in the language of this paper long time ago =-=[27]-=-. However this is not the only way of preserving supersymmetry. For example, we can define a SCFT on any conformally flat curved space just by a conformal mapping from flat space. This is the case of ... |

3 |
Proeyen, “N = 2 supergravity in d
- van
(Show Context)
Citation Context ...ue for general boundaries, where the bulk is only locally asymptotically AdS. 2.1 The multiplet of conformal supergravity The structure of conformal supergravity in 4 dimensions is nicely reviewed in =-=[33]-=-2. The independent field content of the gravity (Weyl) multiplet is gµν ψ i µ T + µν d̃ χ i Aµ0 Aµ i j (2.1) where Aµ0 and Aµ i j = Aµxσ x i j are the gauge fields of the U(1) and SU(2) R-symmetry, re... |

2 |
Uhlemann, “The Boundary Multiplet of N=4
- Ohl, F
(Show Context)
Citation Context ... discussed recently in [9, 11] and seems to be true also for situations with more supersymmetry. In fact, expanding Roman’s N = 4 5d gauged supergravity [29] in an asymptotically AdS space, one finds =-=[30]-=- the conditions of 3 N = 2 superconformal supergravity in four dimensions [31,32] on the boundary. A similar analysis is true for general boundaries, where the bulk is only locally asymptotically AdS.... |

1 |
AGT relation in the light asymptotic limit
- Hama, Hosomichi
(Show Context)
Citation Context ...mal supergravity In order to obtain the Euclidean supersymmetry conditions we have to Wick rotate (2.2). Our strategy is to double the equations and then impose a symplectic Majorana-Weyl 11 See also =-=[40]-=- where further details in this context have been studied. 13 condition on the spinors ( ǫi+ )c = iǫijǫ j + (ǫ−i) c = −iǫijǫ−j (3.1) where (ǫ)c ≡ B−1ǫ∗. ± still denotes chirality. See the appendix A.2 ... |