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## Exploring Curved Superspace

Citations: | 24 - 3 self |

### Citations

760 |
Quantum Field Theory and the
- Witten
- 1989
(Show Context)
Citation Context ...riate choice of U(1)R connection Aµ, we can cancel the U(1)+ component of the spin connection to obtain a scalar supercharge on M. Similarly, it was shown in [33] that the N = 2 twisting procedure of =-=[34]-=- can be interpreted in terms of a certain generalization of (3.12). Equation (3.10) allows us to generalize this argument to an arbitrary Hermitian manifold. Given a complex structure Jµν , the holono... |

551 |
Exact solutions of Einstein’s field equations
- Stephani, Kramer, et al.
- 2003
(Show Context)
Citation Context ...we can introduce SU(2)-invariant one-forms ωa and write the metric as ds2 = dτ2 + hab(τ)ω aωb. The fact that the three Killing vectors are orthogonal implies that hab(τ) = r(τ) 2δab, see for instance =-=[46]-=-. The metric is therefore given by (C.1) and the isometry group is enhanced to SU(2) × SU(2). So far, r(τ) is an arbitrary positive function. In the second case, we can similarly show that the metric ... |

376 | Mirror manifolds and topological field theory
- Witten
(Show Context)
Citation Context ...wo supercharges on Seifert manifolds that are circle bundles over Σ. Rigid supersymmetry on such manifolds was recently discussed in [28,29]. Reducing once more, we make contact with the A-twist on Σ =-=[30,31]-=-. Section 5 describes manifolds admitting two supercharges of equal R-charge. This case turns out to be very restrictive. When M is compact, we will show that it must be hyperhermitian. Using the clas... |

368 | Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” arXiv:0712.2824 [hep-th - Pestun |

251 | Exact Results for Wilson Loops - Kapustin, Willett, et al. - 2010 |

232 |
Topological Sigma Models
- Witten
- 1988
(Show Context)
Citation Context ...wo supercharges on Seifert manifolds that are circle bundles over Σ. Rigid supersymmetry on such manifolds was recently discussed in [28,29]. Reducing once more, we make contact with the A-twist on Σ =-=[30,31]-=-. Section 5 describes manifolds admitting two supercharges of equal R-charge. This case turns out to be very restrictive. When M is compact, we will show that it must be hyperhermitian. Using the clas... |

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

111 |
Rigid Supersymmetric Theories
- Festuccia, Seiberg
(Show Context)
Citation Context ...d spheres. (See [11,12] for some earlier work.) Recently, it was shown that rigid supersymmetry also exists on certain squashed spheres [13-19]. A systematic approach to this subject was developed in =-=[20]-=- using background supergravity. In ordinary supergravity, the metric gµν is dynamical and belongs to a supermultiplet that also includes the gravitino ψµα and various auxiliary fields. Here, we would ... |

94 |
Naturalness versus supersymmetric nonrenormalization theorems, Phys
- Seiberg
- 1993
(Show Context)
Citation Context ...gµν on M. In a supersymmetric theory, the energymomentum tensor resides in a supercurrent multiplet Sµ, which also contains the supersymmetry current Sµα and various other operators. In the spirit of =-=[41]-=- we can promote the background metric gµν to a background supergravity multiplet, which also contains the gravitino ψµα and several auxiliary fields. They couple to the operators in Sµ. In general, th... |

88 | Supersymmetric Yang-Mills theory on a four-manifold,” hep-th/9403193
- Witten
- 1994
(Show Context)
Citation Context ...s to (∇µ − iAµ) ζ = 0 . (1.2) This equation admits a solution if and only if M is Kähler [1]; see also [2]. The relation between twisting and rigid supersymmetry on Kähler manifolds is discussed in =-=[3]-=-. A different generalization of (1.1) arises if we set only the spin-32 component of ∇µζ to zero, ∇µζ = σµη̃ . (1.3) The spinor η̃ is not independent. Rather, it captures the spin-12 component of ∇µζ,... |

68 | A construction of Killing spinors
- Lu, Pope, et al.
- 1999
(Show Context)
Citation Context .... We will now explain how (1.6) arises in the study of supersymmetric field theories on Riemannian manifolds. Following [7-10], much work has focused on supersymmetric theories on round spheres. (See =-=[11,12]-=- for some earlier work.) Recently, it was shown that rigid supersymmetry also exists on certain squashed spheres [13-19]. A systematic approach to this subject was developed in [20] using background s... |

53 | From 4d superconformal indices to 3d partition functions, Phys.Lett. B704 - Dolan, Spiridonov, et al. - 2011 |

52 |
A note on hyper-hermitian four-manifolds
- Boyer
- 1988
(Show Context)
Citation Context ...scribes manifolds admitting two supercharges of equal R-charge. This case turns out to be very restrictive. When M is compact, we will show that it must be hyperhermitian. Using the classification of =-=[32]-=-, this allows us to constrainM to be one of the following: a flat torus T 4, a K3 surface with Ricci-flat Kähler metric, or S3 × S1 with 5 the standard metric ds2 = dτ2 + r2dΩ3 and certain quotients ... |

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

45 | Relation between the 4d superconformal index and the S3 partition function - Imamura |

40 |
Minimal Auxiliary Fields for Supergravity,” Phys
- Stelle, West
- 1978
(Show Context)
Citation Context ...sider variations of definite R-charge. A supercharge δζ of Rcharge +1 corresponds to a solution ζ of (∇µ − iAµ) ζ = −iVµζ − iV νσµνζ , (1.11) 2 The corresponding analysis for old minimal supergravity =-=[23,24]-=- will be described in [25]. See also [26,27]. 3 while a supercharge δ ζ̃ of R-charge −1 corresponds to a solution ζ̃ of (∇µ + iAµ) ζ̃ = iVµζ̃ + iV ν σ̃µν ζ̃ . (1.12) Note that the presence of rigid su... |

33 | The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere, Nucl.Phys. B866 - Martelli, Sparks - 2013 |

32 |
Cohomological localization of Chern-Simons theory
- Källén
(Show Context)
Citation Context ... to be scalars onM. Upon dimensional reduction, they give rise to two supercharges on Seifert manifolds that are circle bundles over Σ. Rigid supersymmetry on such manifolds was recently discussed in =-=[28,29]-=-. Reducing once more, we make contact with the A-twist on Σ [30,31]. Section 5 describes manifolds admitting two supercharges of equal R-charge. This case turns out to be very restrictive. When M is c... |

32 |
Counting chiral primaries in N = 1, d=4 superconformal field theories
- Romelsberger
- 2006
(Show Context)
Citation Context ... + r2dΩ3 , (7.1) where dΩ3 is the round metric on a unit three sphere. As we saw in section 6, this manifold admits four supercharges. Supersymmetric field theories on this space have been studied in =-=[37,38]-=- and more recently in [20]. Here we will examine this example from the point of view of the preceding discussion. Since this manifold admits rigid supersymmetry, it must be Hermitian. We can introduce... |

24 |
Nieuwenhuizen, “The Auxiliary Fields of Supergravity,” Phys
- Ferrara, van
- 1978
(Show Context)
Citation Context ...sider variations of definite R-charge. A supercharge δζ of Rcharge +1 corresponds to a solution ζ of (∇µ − iAµ) ζ = −iVµζ − iV νσµνζ , (1.11) 2 The corresponding analysis for old minimal supergravity =-=[23,24]-=- will be described in [25]. See also [26,27]. 3 while a supercharge δ ζ̃ of R-charge −1 corresponds to a solution ζ̃ of (∇µ + iAµ) ζ̃ = iVµζ̃ + iV ν σ̃µν ζ̃ . (1.12) Note that the presence of rigid su... |

24 |
Rigid supersymmetric theories
- Samtleben, Tsimpis
(Show Context)
Citation Context ...ercharge δζ of Rcharge +1 corresponds to a solution ζ of (∇µ − iAµ) ζ = −iVµζ − iV νσµνζ , (1.11) 2 The corresponding analysis for old minimal supergravity [23,24] will be described in [25]. See also =-=[26,27]-=-. 3 while a supercharge δ ζ̃ of R-charge −1 corresponds to a solution ζ̃ of (∇µ + iAµ) ζ̃ = iVµζ̃ + iV ν σ̃µν ζ̃ . (1.12) Note that the presence of rigid supersymmetry does not depend on the details o... |

23 | Vanishing Theorems and String Backgrounds
- Ivanov, Papadopoulos
(Show Context)
Citation Context ...a hyperhermitian structure on M. In order to establish this result, we will consider the Lee forms associated with Jµν and Iµν , θJµ = Jµ ρ∇νJνρ , θIµ = Iµ ρ∇νIνρ . (5.5) 7 See also the discussion in =-=[35]-=-, where these manifolds are identified with compact Hermitian surfaces for which the restricted holonomy of the Bismut connection is contained in SU(2). 20 Using (3.6) they can be expressed as follows... |

22 | Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories
- Ohta, Yoshida
(Show Context)
Citation Context ... to be scalars onM. Upon dimensional reduction, they give rise to two supercharges on Seifert manifolds that are circle bundles over Σ. Rigid supersymmetry on such manifolds was recently discussed in =-=[28,29]-=-. Reducing once more, we make contact with the A-twist on Σ [30,31]. Section 5 describes manifolds admitting two supercharges of equal R-charge. This case turns out to be very restrictive. When M is c... |

20 |
The tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N=1 supergraity, Nucl.Phys. B198
- Sohnius, West
- 1982
(Show Context)
Citation Context ...are not equivalent and can lead to different backgrounds with rigid supersymmetry. We will focus on theories with a U(1)R symmetry, which can be coupled to the new minimal formulation of supergravity =-=[21,22]-=-.2 In this formulation, the auxiliary fields in the supergravity multiplet consist of an Abelian gauge field Aµ and a two-form gauge field Bµν . The dual field strength V µ of Bµν is a well-defined, c... |

19 |
Killing spinors and SYM on curved spaces
- Blau
- 2000
(Show Context)
Citation Context .... We will now explain how (1.6) arises in the study of supersymmetric field theories on Riemannian manifolds. Following [7-10], much work has focused on supersymmetric theories on round spheres. (See =-=[11,12]-=- for some earlier work.) Recently, it was shown that rigid supersymmetry also exists on certain squashed spheres [13-19]. A systematic approach to this subject was developed in [20] using background s... |

18 | Parallel and Killing spinors on spin(c) manifolds, Commun.Math.Phys - Moroianu - 1997 |

17 |
An Alternative Minimal Off-Shell Version
- Sohnius, West
- 1981
(Show Context)
Citation Context ...the choice of propagating and auxiliary fields. For instance, the FZ-multiplet couples to the old minimal formulation of supergravity [23,24], while the Rmultiplet couples to new minimal supergravity =-=[21,22]-=-. We will focus on the latter. In addition to the metric gµν and the gravitino ψµα, new minimal supergravity contains two auxiliary fields: an Abelian gauge field Aµ and a two-form gauge field Bµν . T... |

16 |
Complex structures on riemannian four-manifolds
- Pontecorvo
- 1997
(Show Context)
Citation Context ... be anti-self-dual. We thus have a compact four-manifold M with anti-self-dual Weyl tensor that admits two Hermitian structures J and I such that J 6= ±I somewhere on M. Applying proposition (3.7) in =-=[36]-=-, it follows that a) The function h in (5.8) is constant. b) The manifold admits a hyperhermitian structure as in (5.3). Moreover, J and I belong to it, and hence they can be expressed in terms of the... |

15 | Reducing the 4d Index to the S3 Partition Function - Gadde, Yan |

12 | Rigidly supersymmetric gauge theories on curved superspace
- Jia, Sharpe
- 2012
(Show Context)
Citation Context ...ercharge δζ of Rcharge +1 corresponds to a solution ζ of (∇µ − iAµ) ζ = −iVµζ − iV νσµνζ , (1.11) 2 The corresponding analysis for old minimal supergravity [23,24] will be described in [25]. See also =-=[26,27]-=-. 3 while a supercharge δ ζ̃ of R-charge −1 corresponds to a solution ζ̃ of (∇µ + iAµ) ζ̃ = iVµζ̃ + iV ν σ̃µν ζ̃ . (1.12) Note that the presence of rigid supersymmetry does not depend on the details o... |

8 | The Nuts and Bolts of Supersymmetric Gauge Theories on Biaxially squashed Three-Spheres,” [arXiv:1111.6930 [hep-th - Martelli, Sparks |

6 |
Dérivées de lie des spineurs, Ann
- Kosmann
- 1972
(Show Context)
Citation Context ...eed the commutator of two covariant derivatives, [∇µ,∇ν]ζ = 1 2 Rµνabσ abζ , [∇µ,∇ν ]ζ̃ = 1 2 Rµνabσ̃ abζ̃ . (A.10) Finally, the Lie derivatives of ζ and ζ̃ along a vector field X = Xµ∂µ are given by =-=[40]-=-, LXζ = Xµ∇µζ − 1 2 ∇µXνσµνζ , LX ζ̃ = Xµ∇µζ̃ − 1 2 ∇µXν σ̃µν ζ̃ . (A.11) Appendix B. Review of Curved Superspace In this appendix we explain how to place a four-dimensional N = 1 theory on a Riemanni... |

3 |
Spin geometry. Princeton mathematical series
- Lawson, Michelsohn
- 1989
(Show Context)
Citation Context ...idered in the literature. For instance, we can twist by a line bundle L. Given a connection Aµ on L, this leads to (∇µ − iAµ) ζ = 0 . (1.2) This equation admits a solution if and only if M is Kähler =-=[1]-=-; see also [2]. The relation between twisting and rigid supersymmetry on Kähler manifolds is discussed in [3]. A different generalization of (1.1) arises if we set only the spin-32 component of ∇µζ t... |

3 |
Supersymmetry In The Space-time R
- Sen
- 1987
(Show Context)
Citation Context ... + r2dΩ3 , (7.1) where dΩ3 is the round metric on a unit three sphere. As we saw in section 6, this manifold admits four supercharges. Supersymmetric field theories on this space have been studied in =-=[37,38]-=- and more recently in [20]. Here we will examine this example from the point of view of the preceding discussion. Since this manifold admits rigid supersymmetry, it must be Hermitian. We can introduce... |

2 |
Topological Quantum Field Theory And N=2
- Karlhede, Rocek
- 1988
(Show Context)
Citation Context ...×SU(2)− with U(1)+ ⊂ SU(2)+. For an appropriate choice of U(1)R connection Aµ, we can cancel the U(1)+ component of the spin connection to obtain a scalar supercharge on M. Similarly, it was shown in =-=[33]-=- that the N = 2 twisting procedure of [34] can be interpreted in terms of a certain generalization of (3.12). Equation (3.10) allows us to generalize this argument to an arbitrary Hermitian manifold. ... |