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

TL;DR

The paper investigates SU(4) Yang–Mills theory at finite temperature using lattice calculations on $N_t=6$ lattices to determine the order of the deconfinement transition and to measure static-string tensions in representations $4$, $6$, $10$, and $15$. It provides clear evidence for a first-order deconfinement transition with a latent heat $\,\Delta\epsilon/\epsilon_{SB}\approx 0.60\pm0.15$, and demonstrates that this transition is well separated from the bulk transition on $N_t=6$. The string-tension analysis reveals distinct fundamental and diquark tensions with $\sigma_2/\sigma_1$ in the range $(1,2)$ and shows adjoint-string breaking at short distances, aligning with expectations from related gauge-theory insights. Overall, the work extends lattice studies to $N_c=4$, clarifies the finite-temperature phase structure, and opens avenues for more precise, higher-$N_c$ investigations.

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 $Δε\approx 0.6 ε_{SB}$. Computing Polyakov loop correlation functions we calculate the string tension at finite temperature in the confined phase between fundamental charges, $σ_1$, between diquark charges, $σ_2$, and between adjoint charges $σ_4$. We find that $1 < σ_2/σ_1 < 2$, and our result for the adjoint string tension $σ_4$ is consistent with string breaking.

Figures (16)

• Figure 1: Columbia diagram ref:CU_2P1, showing the nature of the 2+1-flavor finite temperature transition for different values of $m_{u,d}$ and $m_s$. Regions labeled I have a first-order transition, while the region II has only a crossover. For $m_u=m_d=0$ there is a tri-critical point (square) above which the chiral transition is second-order, denoted by asterisks. The pure glue limit is indicated by the octagon at $(\infty,\infty)$. The question mark indicates the physical $(m_{u,d},m_s)$ according to calculations with staggered fermions ref:KS_2P1. (Ref. ref:WIL_2P1 suggests that the physical point lies lower, in the Region I, when Wilson fermions are used.)
• Figure 2: Phase diagram of fundamental-adjoint lattice action showing the lattice-induced bulk transition. The transition line crosses the fundamental axis for $N_c > 3$.
• Figure 3: Magnitude of the Polyakov loop vs. $\beta$ on a $4\times 8^3$ lattice.
• Figure 4: Plaquette vs. $\beta$ on $4\times 8^3$ lattice. The normalization is such that $\langle U_\mathrm{plaq}\rangle = N_c$ in the free theory.
• Figure 5: Magnitude of the fundamental Polyakov loop vs. $\beta$ on a $6\times 12^3$ lattice.