Double Wick rotating Green-Schwarz strings
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.
Keywords
Cite
@article{arxiv.1412.5137,
title = {Double Wick rotating Green-Schwarz strings},
author = {Gleb Arutyunov and Stijn J. van Tongeren},
journal= {arXiv preprint arXiv:1412.5137},
year = {2015}
}
Comments
v2, updated discussion on target space interpretation, elaborated discussion on minor points, content matches published version, 28 pages, 3 figures