Complex matrix model duality

The same complex matrix model calculates both tachyon scattering for the c=1 noncritical string at the self-dual radius and certain correlation functions of operators which preserve half the supersymmetry in N=4 super-Yang-Mills theory. 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 Kontsevich-Penner 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.