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Exact M-Theory Solutions, Integrable Systems, and Superalgebras
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Exact M-Theory Solutions, Integrable Systems, and Superalgebras
Інший ID:
2010 Mathematics Subject Classification: 81Q60; 17B80
DOI:10.3842/SIGMA.2015.029
DOI:10.3842/SIGMA.2015.029
Посилання:
Exact M-Theory Solutions, Integrable Systems, and Superalgebras / E. D'Hoker // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 48 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
It is a pleasure to thank Constantin Bachas, John Estes, Michael Gutperle, Drya Krym, and Paul
Sorba for fruitful collaborations on the projects reviewed in this paper. I gratefully acknowledge
the warm hospitality and the financial support of the Laboratoire de Physique Th´eorique at
the Ecole Normale Sup´erieure, where part of this work was carried out. Finally, I would like to
acknowledge the organizers, Decio Levi, Willard Miller, Yvan Saint-Aubin, and Pavel Winternitz
for inviting me to the enjoyable conference and celebration in honor of Luc Vinet at the Centre
de Recherches Math´ematiques.
Дата:
2015
Переглядів:
444
Завантажень:
254
Анотація:
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.
