String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories

TL;DR

This paper investigates string tension scaling in high-temperature SU(N) gauge theories with adjoint fermions, revealing a novel Casimir-like scaling law for spatial string tensions derived from semiclassical dual models.

Contribution

It introduces a new scaling behavior for string tensions in high-temperature confining SU(N) theories, connecting perturbative and semiclassical approaches, and distinguishes electric and magnetic tension laws.

Findings

Higher representation string tensions are smaller than the fundamental.

Spatial string tensions follow a Casimir-like scaling law.

Electric and magnetic tension scaling laws differ and are distinguishable.

Abstract

SU(N) gauge theories, extended with adjoint fermions having periodic boundary conditions, are confining at high temperature for sufficiently light fermion mass $m$. In the high temperature confining region, the one-loop effective potential for Polyakov loops has a Z(N)-symmetric confining minimum. String tensions associated with Polyakov loops are calculable in perturbation theory, and display a novel scaling behavior in which higher representations have smaller string tensions than the fundamental representation. In the magnetic sector, the Polyakov loop plays a role similar to a Higgs field, leading to an apparent breaking of SU(N) to $U(1)^{N-1}$. This is turn yields a dual effective theory where magnetic monopoles give rise to string tensions for spatial Wilson loops. The spatial string tensions are calculable semiclassically from kink solutions of the dual system. We show that the spatial string tensions $\sigma^{(s)}_k$ associated with each $N$-ality $k$ obey a variant of Casimir scaling $\sigma^{(s)}_k /\sigma^{(s)}_1 \leq \sqrt{k(N-k)/(N-1)} $. Although lattice simulations indicate that the high temperature confining region is smoothly connected to the confining region of low-temperature pure SU(N) gauge theory, the electric and magnetic string tension scaling laws are different and readily distinguishable.