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′ branes along a self-dual string. These solutions have space-time manifold AdS₃×S³×S³ warped over a Riemann surface Σ, and are invariant under the exceptional Lie superalgebra D(2,1;γ)⊕D(2,1;γ), where γ is a real continuous parameter and |γ| 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 Σ which is of the Liouville sine-Gordon type. Families of regular solutions are distinguished by the sign of γ, and include a two-parameter Janus solution for γ>0, and self-dual strings on M5 as well as asymptotically AdS₄/Z₂ solutions for γ<0.