  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.
