## Gravity/CFT correspondence for three-dimensional Einstein gravity with a conformal scalar field.(English)Zbl 1262.83010

Summary: We study the three-dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newton’s constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martinez-Zanelli solution of Einstein’s equations with a negative cosmological constant coupled to conformal scalar field.

### MSC:

 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 83C57 Black holes 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations

### Keywords:

gravity/CFT correspondence; 3D black holes
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