Abstract
We consider the ABF background underlying the η-deformed AdS5×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 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 invariance 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 invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3×S3×T4and AdS2×S2×T6models.
Highlights
The study of integrable deformations of the AdS5 × S5 superstring sigma model is an important direction in the search for new solvable examples of AdS/CFT duality
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
The usual claim that κ-symmetry implies the corresponding action can be interpreted as that of a GS superstring propagating in a background that is a consistent type II supergravity solution assumes that the κ-symmetry is of the standard GS “projector” form [5]
Summary
The study of integrable deformations of the AdS5 × S5 superstring sigma model is an important direction in the search for new solvable examples of AdS/CFT duality. The HT dilaton φhas a term linearly depending on the isometric directions of Gand F5 and one cannot directly apply the standard T-duality transformation rules [15] to the full HT background to get a full T-dual supergravity solution, and the Weyl invariance of the T-dual sigma model requires further investigation.5 This is consistent with the observation [7] that the ABF background does not satisfy the full set of type IIB supergravity equations. = 0.8 These universal scale invariance conditions will be satisfied by the ABF background for a particular choice of the vectors Xm and Ym. To explain the origin of the second “I -modified” set of equations let us first ignore the R–R fields and assume that there exists the following metric-dilaton background that solves the Weyl invariance equations (i.e. Rmn + 2DmDnφ = 0, βφ = const) ds2 = e2a(x)[dy + Aμ(x)dxμ]2 + gμν (x)dxμdxν ,. In Appendix G we explain how the 2nd-order equations for the R–R couplings F emerge as the one-loop conditions of scale invariance for the GS sigma model (1.2)
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