Supergravity dual of c-extremization

Abstract

Recently a general principle, called c-extremization, which determines the exact R-symmetry of two-dimensional SCFTs with N = (0,2) supersymmetry was identified. In this note we show that the supergravity dual corresponds to the extremization of the T-tensor of N = 2 gauged supergravity in three-dimensions. To support this claim, we demonstrate that the expected central charge of SCFTs arising from twisted compactifications of four-dimensional N = 4 SYM on Riemann surfaces, whose gravity dual is a reduction of five-dimensional U(1)^3 gauged supergravity, is recovered in the three-dimensional framework.