Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$

Abstract

We derive the partition function of an $\mathcal{N}=2$ chiral multiplet on topologically twisted $H^2\times S^1$. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an $H^2\times S^1$ metric containing two parameters: one is the $S^1$ radius, while the other gives a fugacity $q$ for the angular momentum on $H^2$. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of $q$-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable fields reproduces three-dimensional holomorphic blocks.

arXiv comment14 pages, published version, added clarifications, corrected title

References in corpus (25)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Two Dimensional Gauge Theories Revisited
• SUSY Gauge Theories on Squashed Three-Spheres
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Localization techniques in quantum field theories
• Counting Gauge Invariants: the Plethystic Program
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• The Geometry of Supersymmetric Partition Functions
• Localization on Hopf surfaces
• Exact microstate counting for dyonic black holes in AdS4
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Dual Boundary Conditions in 3d SCFT's
• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Black hole entropy in massive Type IIA
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Large AdS black holes from QFT
• N=2 gauge theories on the hemisphere $H{S}^4$
• (0,2) Dynamics From Four Dimensions
• Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
• N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$
• 7D supersymmetric Yang-Mills on curved manifolds
• Supersymmetric Field Theories on AdS_p x S^q

Cited by in corpus (8)

• Monodromy Defects from Hyperbolic Space
• Free energy and defect $C$-theorem in free scalar theory
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Boundary conditions and localization on AdS: Part 2 General analysis
• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$