Phase transition in matrix model with logarithmic action: Toy-model for gluons in baryons

TL;DR

This paper models gluon-quark interactions in baryons using a simplified matrix model, revealing a phase transition that enhances gluon correlations in baryons, shedding light on gluon contributions to proton momentum.

Contribution

It introduces a novel matrix model capturing gluon-quark dynamics and identifies a phase transition relevant to baryon structure and gluon contributions.

Findings

Identifies a phase transition at nu_c=0.27 from one-cut to two-cut eigenvalue distributions.

Shows eigenvalues move away from zero, increasing gluon correlations in baryons.

Demonstrates gluon correlations are enhanced in baryons compared to the vacuum.

Abstract

We study the competing effects of gluon self-coupling and their interactions with quarks in a baryon, using the very simple setting of a hermitian 1-matrix model with action tr A^4 - log det(nu + A^2). The logarithmic term comes from integrating out N quarks. The model is a caricature of 2d QCD coupled to adjoint scalars, which are the transversely polarized gluons in a dimensional reduction. nu is a dimensionless ratio of quark mass to coupling constant. The model interpolates between gluons in the vacuum (nu=infinity), gluons weakly coupled to heavy quarks (large nu) and strongly coupled to light quarks in a baryon (nu to 0). It's solution in the large-N limit exhibits a phase transition from a weakly coupled 1-cut phase to a strongly coupled 2-cut phase as nu is decreased below nu_c = 0.27. Free energy and correlation functions are discontinuous in their third and second derivatives at nu_c. The transition to a two-cut phase forces eigenvalues of A away from zero, making glue-ring correlations grow as nu is decreased. In particular, they are enhanced in a baryon compared to the vacuum. This investigation is motivated by a desire to understand why half the proton's momentum is contributed by gluons.