Supergravity dual of c-extremization

Recently, a general principle, called c-extremization, which determines the exact R symmetry of two-dimensional conformal field theories with N=(0,2) supersymmetry, was identified. In this work 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 conformal field theories arising from twisted compactifications of four-dimensional N=4 Super-Yang-Mills on Riemann surfaces, whose gravity dual is a reduction of five-dimensional U(1) 3 gauged supergravity, is recovered in the three-dimensional framework.