Supergravity dual ofc-extremization

Abstract

Recently, a general principle, called $c$-extremization, which determines the exact $R$ symmetry of two-dimensional conformal field theories with $\mathcal{N}=(0,2)$ supersymmetry, was identified. In this work we show that the supergravity dual corresponds to the extremization of the $T$ tensor of $\mathcal{N}=2$ 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 $\mathcal{N}=4$ 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.