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Enhanced Euclidean supersymmetry, 11D supergravity and $SU(infty)$ Toda equation | | Maciej Dunajski
; Jan Gutowski
; Wafic Sabra
; | | Date: |
9 Jan 2013 | | Abstract: | 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 $SU(infty)$ Toda equation. We give one example of a regular
solution and analyse its supersymmetry.
We also construct and classify solutions to N=2 minimal gauged supergravity
in four Euclidean dimensions (these are the same as Euclidean Einstein-Maxwell
space-times with non-vanishing cosmological constant), where the Killing spinor
equations admit more than one solution and so the supersymmetry is enhanced. If
the Weyl tensor is anti-self-dual then the enhanced supersymmetric metrics are
given by separable solutions to the $SU(infty)$ Toda equation. Otherwise they
are ambi-K"ahler and are conformally equivalent to K"ahler metrics of Calabi
type or to product metrics on two Riemann surfaces. | | Source: | arXiv, 1301.1896 | | Services: | Forum | Review | PDF | Favorites | |
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