Gravity duals of N = 2 superconformal field theories with no electrostatic description

We construct the first eleven-dimensional supergravity solutions, which are regular, have no smearing and possess only SO(2,4) x SO(3) x U(1)_R isometry. They are dual to four-dimensional field theories with 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,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.