2d String Theory and the Non-Perturbative c=1 Matrix Model

Abstract

A valuable testing ground for exploring new features of string theory and quantum gravity is the duality between c=1 string theory and the c=1 matrix quantum mechanics, which has been explored for over 30 years. In this thesis, we use efficient numerical techniques to evaluate Liouville correlation functions and to compute scattering amplitudes of closed strings in string perturbation theory, resolving several previous puzzles in the perturbative duality dictionary. In addition to this, we present a worldsheet formalism for computing all non-perturbative corrections to these amplitudes, which require including disconnected worldsheet diagrams with ZZ-instanton boundary conditions. By matching these contributions against the dual matrix model, we propose the non-perturbative completion of c=1 string theory. We further extend the duality by introducing new degrees of freedom known as long strings, which from the worldsheet description are given by open strings on FZZT branes in a limit where the FZZT branes decouple and the open strings are infinitely stretched. The first few tree-level scattering amplitudes of these objects are computed, and show an impressive agreement with the corresponding amplitudes computed in the dual U(N) matrix quantum mechanics, where long strings are given by states in non-singlet sectors of the U(N) symmetry group.