Double Wick rotating Green-Schwarz strings

TL;DR

This paper establishes conditions under which string theories on different backgrounds are related by double Wick rotations, demonstrating that the AdS_5 x S^5 mirror model corresponds to a transformed background, with implications for integrability in AdS/CFT.

Contribution

It derives transformation laws for background fields under double Wick rotation, extending previous work to include dilaton and RR fields, and applies these to key AdS backgrounds.

Findings

Mirror AdS_5 x S^5 is a string on a transformed background.

Transformation laws are compatible with supergravity equations.

Explicit second-order fermionic action for generic backgrounds is derived.

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.