Two-Dimensional Yang-Mills Theories Are String Theories

Abstract

We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold M can be associated with maps from a string worldsheet onto M. These maps are unbranched and branched covers of M with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in M. These string theories differ from SU(N) YangMills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets. †

Superconformal coset equivalence from level-rank duality

“…Since the group factors SU(k + n) m and SU(k) m+n in G(k, n, m) are level-rank duals of factors in G(m, n, k), the natural map between corresponding representations is Young tableau transposition [13][14][15][16][17]21]:…”

“…This equivalence arises largely as a consequence of the level-rank duality [13,14,15,16,17] of the constituent WZW models.…”

Large N phases of chiral QCD2

“…Two-dimensional pure QCD, however, does admit a nonperturbative exact solution [1][2][3]. Recent work [4][5][6][7][8] has shown further that there is string theory description of pure two-dimensional gauge theories with various gauge groups. It is hoped that some modification of this string picture will provide a systematic nonperturbative description of QCD in any dimension.…”

Exact correlators of giant gravitons from dual $N = 4$ SYM theory

“…The connection between Symmetric and Unitary groups was crucial in the development of the String theory of two-dimensional Yang Mills Theory [17,18,19,20,21,22,23,24] and in certain aspects of Low-dimensional Matrix Models [25,26]. Some key useful results are collected here.…”