Scale invariance of the η-deformed AdS<inf>5</inf>Ã-S5 superstring, T-duality and modified type II equations

Abstract

We consider the ABF background underlying the η -deformed AdS 5 × S 5 sigma model. This back- ground fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Wey l invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η -deformed model is scale invariant. This property follows from the formal relation via T-duality between the η -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 in- variance conditions which for the R–R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF 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, they imply the universal scale invari- ance conditions.