Exact M-theory solutions, integrable systems, and superalgebras

Abstract

In this paper, an overview is presented of the recent construction of fully backreacted half-BPS solutions in 11-dimensional supergravity which correspond to near-horizon geometries of M2 branes ending on, or intersecting with, M5 and M5 0 branes along a self-dual string. These solutions have space-time manifold AdS3× S3× S3warped 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 0 branes. The construction proceeds by mapping the reduced BPS equations onto an integrable f ield 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 AdS 4 /Z2solutions for γ < 0.