Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations

TL;DR

This paper investigates the scale invariance and modified supergravity equations of the eta-deformed AdS5 x S5 superstring background, revealing that it does not satisfy standard IIB supergravity but obeys a modified set of equations linked to T-duality.

Contribution

It introduces a set of modified type IIB supergravity equations that account for eta-deformed backgrounds, extending the understanding of scale invariance beyond standard supergravity.

Findings

The eta-deformed background is scale invariant but not Weyl invariant.

Modified supergravity equations depend on Killing vectors and differ from standard equations.

T-duality relates the eta-deformed model to a background with a linear dilaton, explaining the modifications.

Abstract

We consider the ABF background underlying the eta-deformed AdS5 x S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still correspond to UV finite theory on a flat 2d world-sheet, implying that the eta-deformed model is scale invariant. This property follows from the formal relation via T-duality between the eta-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R-R field strengths are of the second order in derivatives. Surprisingly, we also find that the this background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R-R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after the T-duality, to a modification of type II equations from their standard form. We conjecture that the modified equations should follow from kappa-symmetry of the eta-deformed model. All our observations apply also to eta-deformations of AdS3 x S3 and AdS2 x S2 models.