Deconfinement transition and string tensions in SU(4) Yang-Mills Theory

TL;DR

This paper uses lattice calculations to analyze the deconfinement transition order and string tensions in SU(4) Yang-Mills theory, confirming a first-order transition and exploring string behavior between various charges.

Contribution

It provides the first detailed lattice study of the deconfinement transition order and string tensions in SU(4) Yang-Mills theory, including finite temperature effects and string breaking evidence.

Findings

Confirmed first-order deconfinement transition at specific lattice parameters.

Calculated string tensions for fundamental, diquark, and adjoint charges.

Found the ratio of diquark to fundamental string tension between 1 and 2.

Abstract

We present results from numerical lattice calculations of SU(4) Yang-Mills theory. This work has two goals: to determine the order of the finite temperature deconfinement transition on an $N_t = 6$ lattice and to study the string tensions between static charges in the irreducible representations of SU(4). Motivated by Pisarski and Tytgat's argument that a second-order SU($\infty$) deconfinement transition would explain some features of the SU(3) and QCD transitions, we confirm older results on a coarser, $N_t = 4$, lattice. We see a clear two-phase coexistence signal, characteristic of a first-order transition, at $8/g^2 = 10.79$ on a $6\times 20^3$ lattice, on which we also compute a latent heat of $\Delta\epsilon\approx 0.6 \epsilon_{SB}$. Computing Polyakov loop correlation functions we calculate the string tension at finite temperature in the confined phase between fundamental charges, $\sigma_1$, between diquark charges, $\sigma_2$, and between adjoint charges $\sigma_4$. We find that $1 < \sigma_2/\sigma_1 < 2$, and our result for the adjoint string tension $\sigma_4$ is consistent with string breaking.