The simplest gauge-string duality

Abstract: The large N expansion of two-dimensional Yang-Mills theory (YM2) on a 2D spacetime can be expressed as a generating function of Euler characters of holomorphic maps of string worldsheets to spacetime. Schur-Weyl duality and a classic theorem of Hurwitz connecting combinatorics to holomorphic maps are central to this story. We will review these results from the mid-nineties. We will then describe the connections of this simplest gauge-string duality to recent developments: free fermions and giant gravitons, the role of Brauer algebras in complex Matrix models, and the new holomorphic formulation of the "coupled" expansion of YM2.

Some relevant papers:

hep-th/9303046
Sects. 1-7 of hep-th/9411210
0709.2158
0802.3662
0804.2764