Wrapped Branes and Punctured Horizons

TL;DR

This paper explores supergravity solutions related to wrapped branes on Riemann surfaces, revealing how singular solutions correspond to point-like brane sources and analyzing their dual SCFTs with anomaly matching.

Contribution

It identifies physical interpretations of singular Liouville solutions as point-like branes and constructs explicit AdS$_5$ solutions for M5-branes on punctured Riemann surfaces.

Findings

Singular Liouville solutions correspond to point-like brane sources.

Explicit AdS$_5$ solutions for M5-branes on punctured surfaces are constructed.

Holographic duality is validated through anomaly matching.

Abstract

Large classes of AdS$_p$ supergravity backgrounds describing the IR dynamics of $p$-branes wrapped on a Riemann surface are determined by a solution to the Liouville equation. The regular solutions of this equation lead to the well-known wrapped brane supergravity solutions associated with the constant curvature metric on a compact Riemann surface. We show that some singular solutions of the Liouville equation have a physical interpretation as explicit point-like brane sources on the Riemann surface. We uncover the details of this picture by focusing on $\mathcal{N}=1$ theories of class $\mathcal{S}$ arising from M5-branes on a punctured Riemann surface. We present explicit AdS$_5$ solutions dual to these SCFTs and check the holographic duality by showing the non-trivial agreement of 't Hooft anomalies.