SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane and Scaling Along the Wilson Axis

TL;DR

This study investigates the phase transition behavior in SU(3) lattice gauge theory with fundamental and adjoint actions, revealing a critical endpoint where the $0^{++}$ glueball mass vanishes, indicating a specific continuum limit.

Contribution

It provides evidence for the bulk transition line ending in a critical point and analyzes the scaling behavior of glueball masses near this endpoint.

Findings

The ratio of string tension to critical temperature remains constant along the transition line.

The $0^{++}$ glueball mass decreases approaching the critical endpoint.

Other glueball masses remain unchanged near the endpoint.

Abstract

We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with $N_t=4$, which was found to join onto the bulk transition line at its endpoint, we find that the ratio $\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the $0^{++}$ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint, with the continuum limit there being a $\phi^4$ theory with a diverging correlation length only in the $0^{++}$ channel. We comment on the implications for the scaling behavior along the fundamental or Wilson axis.