Complex matrix model duality

The same complex matrix model calculates both tachyon scattering for the c = 1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N = 4 superYang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian KontsevichPenner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces.