IIB an equivariantly localized puncture

TL;DR

This paper employs equivariant localization to compute observables in AdS3 solutions of type IIB supergravity, introducing a novel boundary-based localization method to analyze punctures and defects in 2d SCFTs.

Contribution

It develops a new localization technique for odd-dimensional internal spaces via boundary contributions, enabling analysis of punctures and defects in supergravity solutions.

Findings

Computed central charges for 2d SCFTs from punctured Riemann surfaces.

Applied localization to study supersymmetric solutions with punctures.

Introduced a boundary-based localization method for internal spaces.

Abstract

We use equivariant localization to compute various observables for $\mathcal{N}=(2,2)$ preserving AdS$_3$ solutions in type IIB supergravity. Our method for localizing the odd-dimensional internal space is to perform a dimensional reduction along a shrinking circle which introduces a boundary in the remaining even-dimensional spacetime. Canonical even-dimensional localization can then be performed on this space after taking into account contributions from the boundary. We illustrate with a number of supersymmetric solutions. One of the novel aspects of this work is applying these techniques to study punctures and defects using localization. We obtain new results for the central charge of 2d SCFTs arising from compactifying $\mathcal{N}=4$ SYM on a punctured Riemann surface.