Exact M-Theory Solutions, Integrable Systems, and Superalgebras

TL;DR

This paper constructs exact supergravity solutions describing intersecting M-branes with rich symmetry, using integrable systems, and explores their geometric and physical properties, including Janus and self-dual string solutions.

Contribution

It introduces a new class of exact 11D supergravity solutions with integrable structures linked to superalgebras, expanding understanding of M-brane intersections.

Findings

Solutions exhibit ${ m AdS}_3 imes S^3 imes S^3$ warped over a Riemann surface

Solutions are invariant under the superalgebra $D(2,1;\gamma) imes D(2,1;\gamma)$

Includes Janus solutions and self-dual strings distinguished by parameter $oldsymbol{ ext{sign}( extgamma)}$

Abstract

In this paper, an overview is presented of the recent construction of fully back-reacted half-BPS solutions in 11-dimensional supergravity which correspond to near-horizon geometries of M2 branes ending on, or intersecting with, M5 and M5$'$ branes along a self-dual string. These solutions have space-time manifold ${\rm AdS}_3 \times S^3 \times S^3$ warped over a Riemann surface $\Sigma$, and are invariant under the exceptional Lie superalgebra $D(2,1;\gamma) \oplus D(2,1;\gamma)$, where $\gamma $ is a real continuous parameter and $|\gamma|$ is governed by the ratio of the number of M5 and M5$'$ branes. The construction proceeds by mapping the reduced BPS equations onto an integrable field theory on $\Sigma$ which is of the Liouville sine-Gordon type. Families of regular solutions are distinguished by the sign of $\gamma$, and include a two-parameter Janus solution for $\gamma >0$, and self-dual strings on M5 as well as asymptotically ${\rm AdS}_4/{\mathbb Z}_2$ solutions for $\gamma <0$.