Two Dimensional QCD coupled to Adjoint Matter and String Theory

TL;DR

This paper explores 2D QCD with adjoint fermions at large N, revealing a deconfinement transition, supersymmetry conditions, and a spectrum of states resembling string theory, with implications for understanding gauge-string duality.

Contribution

It demonstrates the connection between 2D adjoint QCD and string theory, including a deconfinement transition and a spectrum with Regge trajectories, extending the understanding of gauge-string correspondence.

Findings

Deconfinement transition at finite temperature.

Spectrum with approximately linear Regge trajectories.

Exponential growth of state density at high energy.

Abstract

We study $2d$ QCD coupled to fermions in the adjoint representation of the gauge group $SU(N)$ at large $N$, and its relation to string theory. It is shown that the model undergoes a deconfinement transition at a finite temperature (analogous to the Hagedorn transition in string theory), with certain winding modes in the Euclidean time direction turning tachyonic at high temperature. The theory is supersymmetric for a certain ratio of quark mass and gauge coupling. For other values of that ratio, supersymmetry is softly broken. The spectrum of bound states contains an infinite number of approximately linear Regge trajectories, approaching at large mass $M$, $\alpha^\prime M^2=\sum_i i l_i$ $(l_i\in{\bf Z_+})$. Thus, the theory exhibits an exponentially growing density of bosonic and fermionic states at high energy. We discuss these results in light of string expectations.