Four-dimensional Yang-Mills theory with a three-dimensional fermion membrane

TL;DR

This paper investigates the phase structure of four-dimensional Yang-Mills theory with a three-dimensional fermion membrane using lattice simulations, revealing an unconventional phase with spatially nonuniform vacuum properties.

Contribution

It presents the first lattice study of Yang-Mills theory coupled to a fermion membrane, uncovering unique phase behavior not seen in pure Yang-Mills.

Findings

Existence of a spatially nonuniform vacuum phase

Finite Polyakov loop expectation value on the membrane

Exponential decay of the Polyakov loop outside the membrane

Abstract

We study the four-dimensional Yang-Mills theory in the presence of a three-dimensional membrane of fermions by lattice Monte Carlo simulations. We analyze the phase structure of this theory at finite temperature. Below the phase transition temperature of the pure Yang-Mills theory, we obtain an unconventional phase with spatially-nonuniform vacuum. In this phase, the expectation value of the Polyakov loop is finite on the membrane, and it exponentially decays to zero outside the membrane.