Large-N quantum gauge theories in two dimensions

TL;DR

This paper analyzes large-N two-dimensional quantum gauge theories, deriving the saddle point equations, calculating free energy, and discussing implications for higher-dimensional theories.

Contribution

It presents the large-N saddle point solution for 2D quantum gauge theories and explores its relation to the theory's topology and coupling behavior.

Findings

No non-trivial saddle point exists at genus g>0

Free energy depends on area and Euler characteristic

Method may extend to higher dimensions

Abstract

The partition function of a two-dimensional quantum gauge theory in the large-$N$ limit is expressed as the functional integral over some scalar field. The large-$N$ saddle point equation is presented and solved. The free energy is calculated as the function of the area and of the Euler characteristic. There is no non-trivial saddle point at genus $g>0$. The existence of a non-trivial saddle point is closely related to the weak coupling behavior of the theory. Possible applications of the method to higher dimensions are briefly discussed.