More on SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane

TL;DR

This paper investigates the phase transition line in SU(3) lattice gauge theory with fundamental and adjoint actions, providing evidence for its bulk nature and analyzing glueball masses and string tension near the critical endpoint.

Contribution

It offers new insights into the bulk transition line and the behavior of glueball masses, especially the $0^{++}$ state, near the critical endpoint in SU(3) lattice gauge theory.

Findings

The ratio $\,\sqrt{\sigma}/T_c$ remains approximately 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.