Infinite Tension Strings at D>1

TL;DR

This paper explores a matrix model for surfaces in a Bethe lattice, linking it to gauge theory and string models, and analyzes its continuum limit and solutions in external fields.

Contribution

It introduces a matrix model for infinite-tension strings at D>1, connecting it to gauge theory and solving it explicitly in certain cases.

Findings

The model is equivalent to Kazakov-Migdal gauge theory at large N.

In the continuum limit, it is governed by an inverted potential saddle point.

Explicit solutions are provided for the inverted W potential case.

Abstract

A matrix model describing surfaces embedded in a Bethe lattice is considered. From the mean field point of view, it is equivalent to the Kazakov-Migdal induced gauge theory and therefore, at $N=\infty$ and $d>1$, the latter can be interpreted as a matrix model for infinite-tension strings. We show that, in the naive continuum limit, it is governed by the one-matrix-model saddle point with an upside-down potential. To derive mean field equations, we consider the one-matrix model in external field. As a simple application, its explicit solution in the case of the inverted W potential is given.