The Weingarten Model a la Polyakov

TL;DR

This paper generalizes the Weingarten lattice gauge model for Nambu-Goto strings to include intrinsic worldsheet metric fluctuations, reproduces matrix model results in the continuum limit, and explores related models' critical behavior.

Contribution

It introduces a dynamical quadrilation allowing metric fluctuations and connects the model to matrix models and 2D quantum gravity.

Findings

Reproduces hermitian matrix model results for c ≤ 1 matter.

Identifies vortex Wilson lines as non-interacting fermions at c=1.

Analyzes critical behavior of SOS and vertex models coupled to 2D quantum gravity.

Abstract

The Weingarten lattice gauge model of Nambu-Goto strings is generalised to allow for fluctuations of an intrinsic worldsheet metric through a dynamical quadrilation. The continuum limit is taken for $c\leq1$ matter, reproducing the results of hermitian matrix models to all orders in the genus expansion. For the compact $c=1$ case the vortices are Wilson lines, whose exclusion leads to the theory of non-interacting fermions. As a by-product of the analysis one finds the critical behaviour of SOS and vertex models coupled to 2D quantum gravity.