2d QCD and Integrability, Part I: 't Hooft model

Abstract

We study analytic properties and integrable structures of the meson spectrum in large $N_c$ QCD${}_2$. We show that the integral equation that determines the masses of the mesons, often called the 't Hooft equation, is equivalent to finding solutions to a TQ-Baxter equation. Our analysis extends some of previous results by Fateev et al.\ to general quark masses $m=m_1=m_2$, as a perturbative series of the mass parameter. This reformulation, together with its relation to an inhomogeneous Fredholm equation, makes accessible the analytic structure of the spectrum in the complex plane of the quark masses. We also comment on applications of our techniques to non-perturbative topological string partition functions.

74 pages; v3: presentations improved, errors corrected, comparison with arXiv:2409.11324 included

References in corpus (7)

• Symmetries and Strings of Adjoint QCD${}_2$
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• 2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity
• Adjoint Majorana QCD${}_2$ at Finite $N$
• Multicriticality in Yang-Lee edge singularity
• Supersymmetry in QCD${}_2$ coupled to fermions
• Comments on 1+1d QCD with heavy adjoint quarks

Cited by in corpus (4)

• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Mesons in a quantum Ising ladder
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• Meson scattering and tetraquarks in two-dimensional QCD