The Spectrum of a Large N Gauge Theory Near Transition from Confinement to Screening
David J. Gross, Akikazu Hashimoto, Igor R. Klebanov
TL;DR
The paper analyzes the spectrum of a 1+1D large-$N$ gauge theory with an adjoint Majorana fermion, focusing on the confinement-to-screening transition as the fermion mass $m$ tends to zero. Using Discrete Light-Cone Quantization (DLCQ), they argue that the spectrum becomes continuous above a two-particle threshold, with the onset at $m^2=4 m_1^2$ where $m_1$ is the lightest bound-state mass. A decoupling framework shows the massless and massive sectors separate in the $m=0$ limit, organizing the massive sector into KM current blocks and predicting $n$-body thresholds at $m^2=(\sum m_i)^2$. The DLCQ analysis with anti-periodic boundary conditions provides numerical evidence for these ideas, demonstrating convergence and state-tracking behavior that supports the continuum onset and the expected degeneracies between bosonic and fermionic sectors. The work advances understanding of how confinement gives way to screening in low-dimensional gauge theories and offers a concrete numerical avenue to study spectral transitions near criticality.
Abstract
We study the spectrum of 1+1 dimensional large $N$ QCD coupled to an adjoint Majorana fermion of mass $m$. As $m\to 0$ this model makes a transition from confinement to screening. We argue that in this limit the spectrum becomes continuous for mass greater than twice the mass of the lightest bound state. This critical mass is nothing but the threshold for a decay into two lightest states. We present numerical results based on DLCQ that appear to support our claim.