Non-Perturbative Effects in 2-D String Theory or Beyond the Liouville Wall

TL;DR

This paper explores non-perturbative effects in 2D string theory using collective field theory, revealing instantons that induce operators of strength e^{-1/g} and connecting world sheet and space-time descriptions.

Contribution

It introduces a Lorentz invariant extension of collective field theory and identifies instantons that contribute non-perturbatively in 2D string models.

Findings

Discrete sector includes eigenvalue instantons tunneling between vacua

Instantons induce non-perturbative operators of strength e^{-1/g}

Connection between world sheet Liouville theory and space-time effective theory

Abstract

We discuss continuous and discrete sectors in the collective field theory of $d=1$ matrix models. A canonical Lorentz invariant field theory extension of collective field theory is presented and its classical solutions in Euclidean and Minkowski space are found. We show that the discrete, low density, sector of collective field theory includes single eigenvalue Euclidean instantons which tunnel between different vacua of the extended theory. We further show that these ``stringy" instantons induce non-perturbative effective operators of strength $e^{-{1\over g}}$ in the extended theory. The relationship of the world sheet description of string theory and Liouville theory to the effective space-time theory is explained. We also comment on the role of the discrete, low density, sector of collective field theory in that framework.