A String Theory for 2D QCD

Two-dimensional gauge theories with charged matter fields are
useful toy models for studying gauge theory dynamics, particularly for
examining the duality of large N gauge theories to perturbative string
theories. A useful starting point for such studies is pure Yang-Mills
theory, which is exactly solvable. Its 1/N expansion was interpreted as a
string theory by Gross and Taylor, but they did not provide a worldsheet
action for this string theory, and such an action is useful for coupling
it to matter fields. The chiral sector of the Yang-Mills theory can be
written as a sum over holomorphic maps and has useful worldsheet
descriptions, but the full theory includes more general extremal-area
maps; a formal worldsheet action including all these maps in a
“topological rigid string theory” was written by Hořava many years ago,
but various subtleties arise when trying to use it for computations. In
this talk, we will construct a Polyakov-like generalization of Hořava’s
worldsheet action that is well-defined, and we will show how it reproduces
the free limit of the Yang-Mills theory, both by formal arguments and by
explicitly computing its partition function in several cases. We will also
discuss the generalization of this string theory with boundaries,
corresponding to Wilson loops, and we will mention possible ways to
generalize for the finite-coupling gauge theory.