Perturbative and non-perturbative aspects of the two-dimensional string/Yang-Mills correspondence

TL;DR

This paper explores the perturbative and non-perturbative aspects of the two-dimensional Yang-Mills and string theory correspondence, revealing contributions from D1-branes, absence of D0-branes, and a phase transition between different string descriptions.

Contribution

It improves the bosonization approach to derive the YM_2-string correspondence and uncovers non-perturbative effects and phase structure in the theory.

Findings

Identification of D1-brane contributions to YM_2 partition function

Absence of D0-brane effects suggests type 0B string characteristics

Numerical evidence of a phase transition between perturbative and topological string regimes

Abstract

It is known that YM_2 with gauge group SU(N) is equivalent to a string theory with coupling g_s=1/N, order by order in the 1/N expansion. We show how this results can be obtained from the bosonization of the fermionic formulation of YM_2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM_2 partition function of order exp{-kA/(\pi\alpha' g_s)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead stricly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM_2 is described by a perturbative string theory separated from a region where it is described by a topological string theory.