Two-dimensional SCFTs from wrapped branes and c-extremization

We apply c-extremization, whose proof we review in full detail, to study two-dimensional N=(0,2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. We compute the exact central charges of these theories using anomalies and c-extremization. In all cases we also construct AdS3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization.