Localizing Wrapped M5-branes and Gravitational Blocks

TL;DR

This paper computes the off-shell central charge of certain 2D SCFTs from M5-branes wrapping complex manifolds using localization, matching supergravity and field theory results through gravitational blocks.

Contribution

It introduces a method to compute the off-shell central charge via localization, connecting supergravity solutions with field theory anomaly calculations.

Findings

Off-shell central charge matches between supergravity and field theory.

Central charge expressed as a sum of gravitational blocks.

Validation of gravitational block approach in M5-brane configurations.

Abstract

We consider $d=2$, $\mathcal{N}=(0,2)$ SCFTs that can arise from M5-branes wrapping four-dimensional, complex, toric manifolds and orbifolds. We use equivariant localization to compute the off-shell central charge of the dual supergravity solutions, obtaining a result which can be written as a sum of gravitational blocks and precisely agrees with a field theory computation using anomaly polynomials and $c$-extremization.