Type IIB supergravity solution for the T-dual of the eta-deformed AdS_5 x S^5 superstring

TL;DR

This paper constructs an exact type IIB supergravity solution representing a one-parameter deformation of the T-dual of AdS_5 x S^5, revealing new insights into deformed superstring backgrounds and their relations to gauged WZW and Pohlmeyer-reduced models.

Contribution

It provides the first explicit supergravity solution for the T-dual of the eta-deformed AdS_5 x S^5 background, including analysis of its properties and limits.

Findings

The solution involves metric, dilaton, and RR 5-form fields with a simple form in a rotated basis.

The dilaton's linear dependence on isometric coordinates prevents straightforward T-duality reversal.

In the eta -> i limit, backgrounds relate to gauged WZW models and Pohlmeyer-reduced superstring models.

Abstract

We find an exact type IIB supergravity solution that represents a one-parameter deformation of the T-dual of the AdS_5 x S^5 background (with T-duality applied in all 6 abelian bosonic isometric directions). The non-trivial fields are the metric, dilaton and RR 5-form only. The latter has remarkably simple "undeformed" form when written in terms of a "deformation-rotated" vielbein basis. An unusual feature of this solution is that the dilaton contains a linear dependence on the isometric coordinates of the metric precluding a straightforward reversal of T-duality. If we still formally dualize back, we find exactly the metric, B-field and product of dilaton with RR field strengths as recently extracted from the eta-deformed AdS_5 x S^5 superstring action in arXiv:1507.04239. We also discuss similar solutions for deformed AdS_n x S^n backgrounds with n=2,3. In the eta -> i limit we demonstrate that all these backgrounds can be interpreted as special limits of gauged WZW models and are also related to (a limit of) the Pohlmeyer-reduced models of the AdS_n x S^n superstrings.