Quantum Phases of Yang-Mills Matrix Model Coupled to Fundamental Fermions

TL;DR

This paper explores the quantum phase structure of an SU(2) Yang-Mills matrix model with fundamental fermions, revealing critical behavior, superselection sectors, and multiple distinct quantum phases depending on fermion content.

Contribution

It introduces a detailed analysis of quantum criticality and phase structure in a Yang-Mills matrix model coupled to fermions, highlighting the role of gauge field corners and fermionic degeneracies.

Findings

Quantum critical behavior at special gauge configurations.

Existence of superselection sectors in the Hilbert space.

Identification of three to four quantum phases depending on fermion type.

Abstract

By investigating the $SU(2)$ Yang-Mills matrix model coupled to fundamental fermions in the adiabatic limit, we demonstrate quantum critical behaviour at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. As a consequence of our analysis, we show that 2-color QCD coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase.