Localization on $Ad{S}_2\times S^1$

Abstract

Conformal symmetry relates the metric on $Ad{S}_2\times S^1$ to that of $S^3$. This implies that under a suitable choice of boundary conditions for fields on $Ad{S}_2$ the partition function of conformal field theories on these spaces must agree which makes $Ad{S}_2\times S^1$ a good testing ground to study localization on non-compact spaces. We study supersymmetry on $Ad{S}_2\times S^1$ and determine the localizing Lagrangian for $\mathcal{N}=2$ supersymmetric Chern-Simons theory on $Ad{S}_2\times S^1$. We evaluate the partition function of $\mathcal{N}=2$ supersymmetric Chern-Simons theory on $Ad{S}_2\times S^1$ using localization, where the radius of $S^1$ is $q$ times that of $Ad{S}_2$. With boundary conditions on $Ad{S}_2\times S^1$ which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in $Ad{S}_2$, the result for the partition function precisely agrees with that of the theory on the $q$-fold covering of $S^3$.

28 pages

References in corpus (6)

• Towards a derivation of holographic entanglement entropy
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Nonperturbative black hole entropy and Kloosterman sums
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole

Cited by in corpus (15)

• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• Free energy and defect $C$-theorem in free scalar theory
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• One-loop determinants for black holes in 4d gauged supergravity
• Supersymmetric D3/D5 for massive defects on curved space
• Free energy and boundary anomalies on ${\mathbb{S}}^a\times {\mathbb{H}}^b$ spaces
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
• Boundary Conditions and Localization on AdS: Part 1
• The energy-momentum multiplet of supersymmetric defect field theories
• Boundary conditions and localization on AdS: Part 2 General analysis
• Functional Determinants of Radial Operators in $Ad{S}_2$
• On the localization manifold of 5d supersymmetric spinning black holes
• Supersymmetric Localization on dS: Sum over topologies
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$