Enhanced Euclidean supersymmetry, 11D supergravity and SU(∞) Toda equation

A bstract We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of solutions to SU(∞) Toda equation. We give one example...

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Bibliographic Details
Published in:The journal of high energy physics 2013-10, Vol.2013 (10), p.1-20, Article 89
Main Authors: Dunajski, M., Gutowski, J., Sabra, W. A.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Cosmological constant
Elementary Particles
Equivalence
Euclidean geometry
High energy physics
Killing
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Riemann surfaces
String Theory
Supergravity
Supersymmetry
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Summary:A bstract We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of solutions to SU(∞) Toda equation. We give one example of a regular solution and analyse its supersymmetry. We also analyse the integrability conditions of the Killing spinor equations of N = 2 minimal gauged supergravity in four Euclidean dimensions. We obtain necessary conditions for the existence of additional Killing spinors, corresponding to enhancement of supersymmetry. If the Weyl tensor is anti-self-dual then the supersymmetric metrics satisfying these conditions are given by separable solutions to the SU(∞) Toda equation. Otherwise they are ambi-Kähler and are conformally equivalent to Kähler metrics of Calabi type or to product metrics on two Riemann surfaces.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2013)089