A Bilocal Field Approach to the Large-N Expansion of Two-Dimensional (Gauge) Theories

TL;DR

This paper introduces a bilocal field formalism to unify the large-N expansion approach for various two-dimensional gauge theories, including models with fermionic and bosonic matter, providing exact spectral equations.

Contribution

It develops a general bilocal field framework for large-N expansions in 2D gauge theories, unifying different models and deriving exact particle spectrum equations.

Findings

Unified large-N expansion formalism for 2D gauge theories.

Derived exact equations for particle spectra in these models.

Established correspondence with previous approaches in O(N) models.

Abstract

We consider a wide class of two-dimensional models as gauge theories, Gross-Neveu model, $O(N)$ and $CP^{N-1}$-like models using a formalism based on the introduction of bilocal fields that permits to perform easily the large-N expansion of this set of models in a unified and general way. We mainly discuss the $SU(N)$ gauge field theory minimally coupled to fermionic plus bosonic matter in the fundamental representation, and we obtain within the path integral approach exact equations for the particle spectrum, also in presence of renormalizable polynomial potentials. Finally, we discuss the correspondence between this new approach and the one previously used in the context of the $O(N)$ vector models.