String hamiltonian from generalized YM gauge theory in two dimensions

TL;DR

This paper derives a string Hamiltonian for a generalized two-dimensional SU(N) Yang-Mills theory by bosonizing a fermionic formulation, revealing new interaction vertices in the string description.

Contribution

It extends the known string Hamiltonian formulation from standard YM to generalized YM theories, introducing new interaction vertices.

Findings

Derived a string Hamiltonian for generalized YM theory

Expressed the Hamiltonian in bosonic modes as string creation and annihilation operators

Identified new interaction vertices in the string description

Abstract

Two dimensional SU(N) Yang-Mills theory is known to be equivalent to a string theory, as found by Gross in the large N limit, using the 1/N expansion. Later it was found that even a generalized YM theory leads to a string theory of the Gross type. In the standard YM theory case, Douglas and others found the string hamiltonian describing the propagation and the interactions of states made of strings winding on a cylindrical space-time. We address the problem of finding a similar hamiltonian for the generalized YM theory. As in the standard case we start by writing the theory as a theory of free fermions. Performing a bosonization, we express the hamiltonian in terms of the modes of a bosonic field, that are interpreted as in the standard case as creation and destruction operators for states of strings winding around the cylindrical space-time. The result is similar to the standard hamiltonian, but with new kinds of interaction vertices.