AdS$_3$ from M-branes at conical singularities

TL;DR

This paper generalizes known supersymmetric M-theory solutions involving AdS3 and S3 geometries by introducing M5 branes with M2 charge and conical defects, revealing a relation between the defect's deficit angle and M2 charge.

Contribution

It extends existing solutions by incorporating conical defects and M2 charge in M5 brane backgrounds, providing new insights into the geometry of M-theory solutions.

Findings

Established a relation between conical defect angle and M2 charge.

Constructed more general supersymmetric solutions with defects.

Enhanced understanding of M-brane configurations in AdS3 geometries.

Abstract

M-theory is known to possess supersymmetric solutions where the geometry is $\mathrm{AdS}_3\times S^3\times S^3$ warped over a Riemann surface $\Sigma_{2}$. The simplest examples in this class can be engineered by placing M2 and M5 branes as defects inside of a stack of background M5 branes. In this paper we show that a generalization of this construction yields more general solutions in the aforementioned class. The background branes are now M5's carrying M2 brane charge, while the defect branes are now placed at the origin of a flat hyperplane with a conical defect. The equations of motion imply a relation between the deficit angle produced by the conical defect and the M2 charge carried by the background branes.