U(N) Gauge Theory and Lattice Strings

TL;DR

This paper reformulates U(N) lattice gauge theory as a string theory of random surfaces with singularities, showing that in the large N limit the strings become noninteracting and exploring phase transitions in four dimensions.

Contribution

It introduces a modified lattice string model with pointlike singularities and demonstrates the noninteracting nature of strings at large N, linking gauge theory phases to string world sheet features.

Findings

Strings become noninteracting as N approaches infinity.

Weak coupling phase characterized by spontaneous creation of 'windows' on the string world sheet.

In 4D, the gauge theory exhibits a first order phase transition separating different coupling regimes.

Abstract

We explain, in a slightly modified form, an old construction allowing to reformulate the U(N) gauge theory defined on a D-dimensional lattice as a theory of lattice strings (a statistical model of random surfaces). The world surface of the lattice string is allowed to have pointlike singularities (branch points) located not only at the sites of the lattice, but also on its links and plaquettes. The strings become noninteracting when $N\to\infty$. In this limit the statistical weight a world surface is given by exp[ $-$ area] times a product of local factors associated with the branch points. In $D=4$ dimensions the gauge theory has a nondeconfining first order phase transition dividing the weak and strong coupling phase. From the point of view of the string theory the weak coupling phase is expected to be characterized by spontaneous creation of ``windows'' on the world sheet of the string.