Localizing punctures in M-theory

TL;DR

This paper employs equivariant localization and holography to analyze 4D $ ext{N}=1$ superconformal field theories from M5-branes on punctured Riemann surfaces, revealing how punctures contribute to the central charge.

Contribution

It introduces a method to localize puncture contributions in M-theory setups, generalizing previous results to $ ext{N}=1$ preserving punctures.

Findings

Central charge includes bulk and puncture contributions.

Generalization of known $ ext{N}=2$ puncture results.

New results for $ ext{N}=1$ preserving punctures.

Abstract

We use equivariant localization and holography to study four-dimensional $\mathcal{N}=1$ superconformal field theories arising from M5-branes wrapped on a punctured Riemann surface. We explain how, given a Riemann surface with marked points, one can glue in a ``puncture geometry'' locally around each point. Using equivariant localization we show that the central charge consists of a bulk contribution plus localized puncture contributions. We recover and generalize the known results for locally $\mathcal{N}=2$ preserving punctures, and derive new results for genuinely locally $\mathcal{N}=1$ preserving punctures.