Spacetimes for \lambda-deformations

TL;DR

This paper explores -deformations of 2D conformal field theories, embedding them into string backgrounds satisfying supergravity equations, and provides explicit examples including black hole and AdS/CFT related models.

Contribution

It demonstrates how -deformations can be realized as consistent string backgrounds solving supergravity equations, extending their understanding beyond previous conjectures.

Findings

-deformations can be embedded as full string backgrounds.

Explicit examples include deformations of the SL(2,R)/U(1) black-hole CFT.

The work connects -deformations to known string theory solutions.

Abstract

We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These {\lambda}-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G or, between a G/H gauged WZW model and the non-Abelian T-dual of the geometric coset G/H. {\lambda}-deformations have been conjectured to represent quantum group q-deformations for the case where the deformation parameter is a root of unity. In this work we show how such deformations can be given an embedding as full string backgrounds whose target spaces satisfy the equations of type-II supergravity. One illustrative example is a deformation of the Sl(2,R)/U(1) black-hole CFT. A further example interpolates between the $\frac{SU(2)\times SU(2)}{SU(2)}\times\frac{SL(2,R)\times SL(2,R)}{SL(2,R)} \times U(1)^4$ gauged WZW model and the non-Abelian T-dual of $AdS_3\times S^3\times T^4$ supported with Ramond flux.