2d QCD and Integrability, Part II: Generalized QCD

TL;DR

This paper extends integrability analysis to generalized large N_c QCD2 theories, revealing complex spectral structures, multi-critical points, and conditions for a positive discrete meson spectrum.

Contribution

It introduces a generalized framework for QCD2, recasts the spectral problem into a TQ-Baxter form, and explores the spectral analytic structure across various couplings.

Findings

Identified regions with positive, discrete meson spectra.

Discovered multi-sheeted spectral structures with multi-critical points.

Showed persistence of spectral features in large-representation limits.

Abstract

We extend the study of integrable structures and analyticity of the spectrum in large $N_c$ QCD$_2$ to a broad class of theories called the generalized QCD, which are given by the Lagrangian $\mathcal{L}\propto {\rm tr}\,B\wedge F- {\rm tr}\,V(B)$ coupled to quarks in the fundamental representation. We recast the Bethe-Salpeter equation for the meson spectrum into a TQ-Baxter equation and determine a transfer matrix in a closed form for any given polynomial $V(B)$. Using an associated Fredholm equation, we numerically study the analytic structures of the spectrum as a function of the coefficients of $V(B)$. We determine the region of couplings where the theory admits a positive and discrete spectrum of mesons. Furthermore, we uncover a multi-sheeted structure with infinitely many multi-critical points, where several mesons become simultaneously massless. Lastly, we illustrate that this structure persists in the large-representation limit of the generalized QCD with the SU(2) gauge group.