2d QCD and Integrability, Part II: Generalized QCD

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 $\mathcal{L}\propto \mathrm{tr}B\wedge F-\mathrm{tr}V(B)$ 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.

arXiv comment54 pages; v3: references added, section 3.5 rewritten