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

Benjamin Assel; Dario Martelli; Sameer Murthy; Daisuke Yokoyama

doi:10.1007/JHEP03(2017)095

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

Benjamin Assel^*, Dario Martelli, Sameer Murthy, Daisuke Yokoyama

^*Corresponding author for this work

King's College London

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

173 Downloads (Pure)

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 AdS₃. 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.

Original language	English
Article number	95
Number of pages	64
Journal	Journal of High Energy Physics
Volume	2017
Issue number	3
DOIs	https://doi.org/10.1007/JHEP03(2017)095
Publication status	Published - 17 Mar 2017

Keywords

Chern-Simons Theories
Field Theories in Lower Dimensions
Supersymmetric Gauge Theory

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10.1007/JHEP03(2017)095Licence: CC BY

Localization of supersymmetric field_ASSEL_Accepted 11 Mar 17_GOLD VoR_CC-BYFinal published version, 985 KBLicence: CC BY

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N2 - 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 AdS3. 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.

AB - 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 AdS3. 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.

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

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Keywords

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