# Phases of circle-compactified QCD with adjoint fermions at finite density

## TL;DR

This paper investigates how chemical potential influences confinement, mass gap, and phase transitions in adjoint QCD with one spatial compact dimension, revealing alternating phases and novel superfluid phenomena.

## Contribution

It introduces a detailed analysis of phase structure and nonperturbative effects in adjoint QCD at finite density with a compact dimension, including new insights into superfluid transitions and BEC-BCS crossover.

## Key findings

- Alternating center-symmetric and center-broken phases with increasing chemical potential.
- Photon mass gap in the magnetic bion plasma grows with chemical potential.
- Possible superfluid transition leading to a nonperturbative energy gap for quarks.

## Abstract

We study chemical-potential dependence of confinement and mass gap in QCD with adjoint fermions in spacetime with one spatial compact direction. By calculating the one-loop effective potential for the Wilson line in the presence of chemical potential, we show that a center-symmetric phase and a center-broken phase alternate when the chemical potential in unit of the compactification scale is increased. In the center-symmetric phase we use semiclassical methods to show that photons in the magnetic bion plasma acquire a mass gap that grows with the chemical potential as a result of anisotropic interactions between monopole-instantons. For the neutral fermionic sector which remains gapless perturbatively, there are two possibilities at non-perturbative level. Either to remain gapless (unbroken global symmetry), or to undergo a novel superfluid transition through a four-fermion interaction (broken global symmetry). If the latter is the case, this leads to an energy gap of quarks proportional to a new nonperturbative scale $L^{-1}\exp[-1/(g^4 \mu L)]$, where $L$ denotes the circumference of $S^1$, the low-energy is described as a Nambu-Goldstone mode associated with the baryon number, and there exists a new type of BEC-BCS crossover of the diquark pairing as a function of the compactification scale at small chemical potential.