Exact Two-Dimensional Superconformal R Symmetry and c Extremization

We uncover a general principle dubbed c extremization, which determines the exact R symmetry of a two-dimensional unitary superconformal field theory with N=(0,2) supersymmetry. To illustrate its utility, we study superconformal theories obtained by twisted compactifications of four-dimensional N=4 super–Yang-Mills theory on Riemann surfaces and construct their gravity duals.