Supergrassmannian and large N limit of quantum field theory with bosons and fermions

TL;DR

This paper explores the large N limit of 2D Yang-Mills theory with bosons and fermions, revealing a classical Hamiltonian framework on a supergrassmannian and deriving mesonic spectra via approximations.

Contribution

It extends Rajeev’s approach to include fermions, describing the large N limit as a classical system on an infinite-dimensional supergrassmannian.

Findings

Derivation of 't Hooft equations for mesonic spectrum

Description of the limiting theory as a classical Hamiltonian system

Discussion of alternative approximation schemes

Abstract

We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.