Universal and Nonperturbative Behavior in the One-Plaquette Model of Two-Dimensional String Theory

TL;DR

This paper investigates a one-plaquette model in 2D string theory, revealing nonperturbative effects and a convergent series representation of the density of states, bridging perturbative and nonperturbative regimes.

Contribution

It introduces a nonperturbative analysis of the one-plaquette Hamiltonian, deriving a convergent series for the density of states that incorporates both perturbative and nonperturbative effects.

Findings

The free energy matches a string partition function with discretized world sheets.

Derived a nonperturbative density of states using WKB wave functions.

The series representation converges and includes both perturbative and nonperturbative contributions.

Abstract

The one-plaquette Hamiltonian of large N lattice gauge theory offers a constructive model of a $1+1$-dimensional string theory with a stable ground state. The free energy is found to be equivalent to the partition function of a string where the world sheet is discretized by even polygons with signature and the link factor is given by a non-Gaussian propagator. At large, but finite, N we derive the nonperturbative density of states from the WKB wave function and the dispersion relations. This is expressible as an infinite, but convergent, series with the inverse of the hypergeometric function replacing the harmonic oscillator spectrum of the $1+1$-dimensional string. In the scaling limit, the series is shown to be finite, containing both the perturbative (asymptotic) expansion of the inverted harmonic oscillator model, and a nonperturbative piece that survives the scaling limit.