Exact M-Theory Solutions, Integrable Systems, and Superalgebras

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${}^{\prime }$ branes along a self-dual string. These solutions have space-time manifold ${\mathrm{AdS}}_3\times S^3\times S^3$ 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${}^{\prime }$ 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 ${\mathrm{AdS}}_4/{\mathbb{Z}}_2$ solutions for $\gamma <0$.

This paper is dedicated to Luc Vinet on the occasion of his 60-th birthday

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Cited by in corpus (1)

• Spinor flows with flux, I: short-time existence and smoothing estimates