Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds

Abstract

We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS${}_3$. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.

v3:79p, minor clarifications and references added

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Cited by in corpus (16)

• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• One-loop determinants for black holes in 4d gauged supergravity
• Free energy and boundary anomalies on ${\mathbb{S}}^a\times {\mathbb{H}}^b$ spaces
• Stochastic Lagrangian Dynamics of Vorticity. II. Channel-Flow Turbulence
• Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
• Boundary Conditions and Localization on AdS: Part 1
• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• The energy-momentum multiplet of supersymmetric defect field theories
• Boundary conditions and localization on AdS: Part 2 General analysis
• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
• Localization on $Ad{S}_3\times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity
• Supersymmetric Localization on dS: Sum over topologies
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$