| Abstract: It is well known that the 't Hooft model, 2d QCD at large Nc, represents a unique toy model for exploring the dynamics of mesons. In this talk, based on joint works with S. Komatsu, I will illustrate that the 't Hooft equation determining the masses of mesons of this model, is equivalent to finding solutions to a TQ-Baxter equation. This illustrates a rich analytical structure of the spectrum in the complex plane of the quark masses, allow us to extract analytical expansions for the mesons' masses and study the critical points of the theory.
We extend these results to the generalized QCD_2, obtained by replacing the gluon kinetic term by BF + V(B) for an adjoint scalar B. For any given V(B), we show that the 't Hooft equation is equivalent to a TQ-system that we determine in a closed form and solve asymptotically for the meson masses. This initiates a systematic novel study of the phases and critical point of the theory in the space of the gYM couplings and quark masses.
I will conclude by discussing how identical results can be derived for SU(2) (Generalized) YM theories coupled to fermions in Large J representations. |