The 't Hooft model on (A)dS2
Abstract
We solve large-N two-dimensional QCD with fundamental quarks---the 't Hooft model---on rigid AdS2 and dS2. Their isometries preserve the null gauge A-=0 and in affine coordinates the curvature enters the light-front Hamiltonian only through the special-conformal generator of the null line. The SL(2,ℝ) Casimir then results in an exact meson equation: 't Hooft's equation plus a Legendre operator whose sign is determined by the curvature. On AdS2 it is related to equations proposed in the context of folded/segmented strings and light-front holography. The pion is massless in the chiral limit and obeys a Gell-Mann--Oakes--Renner relation that fixes the chiral condensate, the dimensions cross over from Regge to logarithmic growth once the flux tube exceeds the curvature radius, and the flat-space integrable structure survives. We also solve the problem of a quark interacting with an antiquark placed at the boundary: beyond a critical coupling the string pulls it back to the boundary, resulting in a scattering phase. On dS2 and due to the expansion of space, the mesons are unstable resonances even at N=∞ and eventually dissociate. Their widths are given by Boltzmann factors at the de Sitter temperature.
BibTeX
@misc{betzios2026hooft,
title = {{The 't Hooft model on (A)dS$_2$}},
author = {Panos Betzios},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37667},
eprint = {2610.37667},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37667},
}
RIS
TY - UNPB
TI - The 't Hooft model on (A)dS_2
AU - Panos Betzios
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37667
UR - https://arxiv.org/abs/2610.37667
AB - We solve large-N two-dimensional QCD with fundamental quarks---the 't Hooft model---on rigid AdS_2 and dS_2. Their isometries preserve the null gauge A_-=0 and in affine coordinates the curvature enters the light-front Hamiltonian only through the special-conformal generator of the null line. The SL(2,ℝ) Casimir then results in an exact meson equation: 't Hooft's equation plus a Legendre operator whose sign is determined by the curvature. On AdS_2 it is related to equations proposed in the context of folded/segmented strings and light-front holography. The pion is massless in the chiral limit and obeys a Gell-Mann--Oakes--Renner relation that fixes the chiral condensate, the dimensions cross over from Regge to logarithmic growth once the flux tube exceeds the curvature radius, and the flat-space integrable structure survives. We also solve the problem of a quark interacting with an antiquark placed at the boundary: beyond a critical coupling the string pulls it back to the boundary, resulting in a scattering phase. On dS_2 and due to the expansion of space, the mesons are unstable resonances even at N=∞ and eventually dissociate. Their widths are given by Boltzmann factors at the de Sitter temperature.
ER -