Kerr–Schild perturbations of coset CFTs as scale invariant integrable σ-models

Abstract

Kerr–Schild perturbations in General Relativity provide a fruitful way of constructing new exact solutions starting from known ones, elucidating also the structure of the spacetimes. We initiate such a study in the context of string theory and supergravity. Specifically, we explicitly construct Kerr–Schild perturbations of coset CFTs based on low dimensionality orthogonal groups. We show that these give rise to scale, but not Weyl, invariant integrable σ-models. We explicitly demonstrate that these models can also be derived from a particular limiting procedure of λ-deformed coset CFTs based on non-compact groups. The target space of the simplest σ-model describes a two-dimensional scale invariant black hole for which we also provide two different embeddings to type-II supergravity.