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arXiv · 1412.5137

Double Wick rotating Green-Schwarz strings

Gleb Arutyunov·Stijn J. van Tongeren
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Abstract

Via an appropriate field redefinition of the fermions, we find a set of conditions under which light cone gauge fixed world sheet theories of strings on two different backgrounds are related by a double Wick rotation. These conditions take the form of a set of transformation laws for the background fields, complementing a set of transformation laws for the metric and B field we found previously with a set for the dilaton and RR fields, and are compatible with the supergravity equations of motion. Our results prove that at least to second order in fermions, the AdS_5 x S^5 mirror model which plays an important role in the field of integrability in AdS/CFT, represents a string on `mirror AdS_5 x S^5', the background that follows from our transformations. We discuss analogous solutions for AdS_3 x S^3 x T^4 and AdS_2 x S^2 x T^6. The main ingredient in our derivation is the light cone gauge fixed action for a string on an (almost) completely generic background, which we explicitly derive to second order in fermions.

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Gleb Arutyunov, Stijn J. van Tongeren. 2015-05-05. Double Wick rotating Green-Schwarz strings. https://doi.org/10.1007/jhep05(2015)027

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