Localization of supersymmetric Chern-Simons-Matter theory on a squashed S 3 with SU(2) × U(1) isometry

167

415

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z M . Our primary focus is the dependence of Z M on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries. For N = 1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. We find that Z M is independent of the metric and depends holomorphically on the complex structure moduli. Background gauge fields define holomorphic vector bundles over M and Z M is a holomorphic function of the corresponding bundle moduli. We also carry out a parallel analysis for three-dimensional N = 2 theories with a U(1) R symmetry, where the necessary geometric structure on M is a transversely holomorphic foliation (THF) with a transversely Hermitian metric. Again, we find that Z M is independent of the metric and depends holomorphically on the moduli of the THF. We discuss several applications, including manifolds diffeomorphic to S 3 ×S 1 or S 2 ×S 1 , which are related to supersymmetric indices, and manifolds diffeomorphic to S 3 (squashed spheres). In examples where Z M has been calculated explicitly, our results explain many of its observed properties.

Section: Jhep01(2014)124mentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Squashed Spheresmentioning

confidence: 99%

See 1 more Smart Citation

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

167

415

“…Following the work of Pestun [4], the method has been applied to a large number of theories in two [5][6][7][8], three [9][10][11][12][13][14][15] four [16,17], and five dimensions, [18][19][20][21][22][23][24]. This development went hand-in-hand with an increased interest in theories with rigid supersymmetry on curved manifolds [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone

Schmude

2015

Abstract:We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting holomorphic functions on the associated Calabi-Yau cone. This observation allows us to use standard techniques developed in the context of quiver gauge theories to obtain explicit results for a number of examples; namely S 5 ,

“…For recent developments on localization on three sphere or deformed three spheres, see [18][19][20][21][22].…”

Section: Jhep03(2014)127mentioning

confidence: 99%

Three-dimensional SCFT on conic space as hologram of charged topological black hole

Huang

Rey

Zhou

2014

We construct three-dimensional N = 2 supersymmetric field theories on conic spaces. Built upon the fact that the partition function depends solely on the Reeb vector of the Killing vector, we propose that holographic dual of these theories are fourdimensional, supersymmetric charged topological black holes. With the supersymmetry localization technique, we study conserved supercharges, free energy, and supersymmetric Rényi entropy. At planar large N limit, we demonstrate perfect agreement between the superconformal field theories and the supersymmetric charged topological black holes.