Quantum phase transitions and new scales in QCD-like theories

TL;DR

This paper reveals new dynamical scales and phenomena in confining gauge theories on ${ m R}^3 imes S^1$, showing phase transitions at scales different from the strong scale, with implications for confinement and holographic models.

Contribution

It demonstrates the existence of new scales and phase transitions in QCD-like theories formulated on ${ m R}^3 imes S^1$, challenging previous assumptions about entanglement of symmetries.

Findings

Chiral phase transitions occur at $rac{ ext{Lambda}^{-1}}{N_c}$ without changing center symmetry.

New phenomena and scales are identified outside the reach of holographic models.

Large $N_c$ volume independence confirms the existence of these new scales.

Abstract

It is commonly believed that in confining vector-like gauge theories the center and chiral symmetry realizations are parametrically entangled, and if phase transitions occur, they must take place around the strong scale $\Lambda^{-1}$ of the gauge theory. We demonstrate that (non-thermal) vector-like theories formulated on ${\mathbb R}^{3} \times S^1$ where $S^1$ is a spatial circle exhibit new dynamical scales and new phenomena. There are chiral phase transitions taking place at $\Lambda^{-1}/N_c$ in the absence of any change in center symmetry. $\Lambda^{-1}/N_c$, invisible in (planar) perturbation theory, is also the scale where abelian versus non-abelian confinement regimes meet. Large $N_c$ volume independence (a working Eguchi-Kawai reduction) provides new insights and independently confirms the existence of these scales. We show that certain phases and scales are outside the reach of holographic (supergravity) modeling of QCD.