Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 029, 20 pages      arXiv:1411.6170      https://doi.org/10.3842/SIGMA.2015.029
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet

Exact M-Theory Solutions, Integrable Systems, and Superalgebras

Eric D'Hoker
Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA

Received January 05, 2015, in final form April 03, 2015; Published online April 11, 2015

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 $\gamma <0$.

Key words: M-theory; branes; supersymmetry; superalgebras; integrable systems.

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