PARTITION FUNCTIONS OF MATRIX MODELS: FIRST SPECIAL FUNCTIONS OF STRING THEORY

Abstract

Even though matrix model partition functions do not exhaust the entire set of τ-functions relevant for string theory, they seem to be elementary building blocks for many others and they seem to properly capture the fundamental symplicial nature of quantum gravity and string theory. We propose to consider matrix model partition functions as new special functions. Here we restrict our consideration to the finite-size Hermitian 1-matrix model and concentrate mostly on its phase/branch structure arising when the partition function is considered as a D-module. We discuss the role of the CIV–DV prepotential (as generating a possible basis in the linear space of solutions to the Virasoro constraints, but with a lack of understanding of why and how this basis is distinguished).