Exploring curved superspace (II)

Abstract:We study Higgs branch localization of N = 2 supersymmetric theories placed on compact Euclidean manifolds. We analyze the resulting localization equations in detail on the four-sphere and find that in this case the path integral is dominated by vortex-like configurations as well as singular Seiberg-Witten monopoles located at the north and south pole. The partition function is written accordingly.

Section: Killing Spinors and Complex Structuresmentioning

confidence: 90%

Ellipsoid partition function from Seiberg-Witten monopoles

Pan

Peelaers

2015

“…They can therefore be coupled to different background supergravity fields, which give rise to different classes of supersymmetric manifolds M. See [1,[8][9][10][11] for a discussion in four dimensions. 4 In the presence of continuous Abelian flavor symmetries that can mix with the R-symmetry, the Rmultiplet is not unique.…”

Section: A (R)mentioning

confidence: 99%

“…From the corresponding formula in new minimal supergravity, 11) where F µν = ∂ µ A ν − ∂ ν A µ is the field strength of A µ . Using the fact that ζ α determines the complex structure through (1.6) and the nowhere vanishing (2, 0)-form ζσ µν ζ, we find that setting (1.11) to zero implies the following constraints,…”

Section: Background Vector Fields In Four Dimensionsmentioning

confidence: 99%

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

Self Cite

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.

“…These 4-manifolds can preserve 2 supercharges with opposite R-charge and a holomorphic Killing vector generating the torus action on M 4 [2][3][4]. 1 General results [6,7] state that partition functions on these spaces do not depend on the Hermitian metric but are holomorphic functions of the complex structure parameters and of the background gauge fields through the corresponding vector bundles.…”

Section: Introductionmentioning

confidence: 99%

Factorisation and holomorphic blocks in 4d

Nieri

Pasquetti

2015

165

We study N = 1 theories on Hermitian manifolds of the form M 4 = S 1 × M 3 with M 3 a U(1) fibration over S 2 , and their 3d N = 2 reductions. These manifolds admit an Heegaard-like decomposition in solid tori D 2 × T 2 and D 2 × S 1 . We prove that when the 4d and 3d anomalies are cancelled, the matrix integrands in the Coulomb branch partition functions can be factorised in terms of 1-loop factors on D 2 × T 2 and D 2 × S 1 respectively. By evaluating the Coulomb branch matrix integrals we show that the 4d and 3d partition functions can be expressed as sums of products of 4d and 3d holomorphic blocks.