Gravity duals of $ \mathcal{N} $ = 2 superconformal field theories with no electrostatic description

Abstract

Abstract We construct the first eleven-dimensional supergravity solutions, which are regular, have no smearing and possess only SO(2, 4) × SO(3) × U(1) R isometry. They are dual to four-dimensional field theories with $ \mathcal{N} $ = 2 superconformal symmetry. We utilise the Toda frame of self-dual four-dimensional Euclidean metrics with SU(2) rotational symmetry. They are obtained by transforming the Atiyah-Hitchin instanton under SL(2, $ \mathbb{R} $ ) and are expressed in terms of theta functions. The absence of any extra U(1) symmetry, even asymptotically, renders inapplicable the electrostatic description of our solution.