Phase diagram of Yang-Mills theories in the presence of a theta term

TL;DR

This work investigates how the deconfinement temperature in pure SU($N$) Yang–Mills theory depends on a topological theta term, using lattice methods that include analytic continuation from imaginary $\theta$ and reweighting to real $\theta$. The authors provide a cross-validated determination of the curvature $R_\theta$ of $T_c(\theta)$ for $N=3$, finding $R_\theta \approx 0.0178(5)$ in the continuum, and show nontrivial topological-background effects on $T_c$ and the Polyakov loop. They also discuss a qualitative phase diagram in the $T$–$\theta$ plane, drawing analogies to QCD at imaginary baryon chemical potential and proposing a large-$N$-based multi-branched structure at low $T$ versus smooth, periodic behavior at high $T$, with potential duality between the two pictures. The results inform our understanding of theta dependence in non-Abelian gauge theories and its connections to topological and deconfinement physics, with implications for the large-$N$ limit and related models.

Abstract

We study the phase diagram of non-Abelian pure gauge theories in the presence of a topological theta term. The dependence of the deconfinement temperature on theta is determined on the lattice both by analytic continuation and by reweighting, obtaining consistent results. The general structure of the diagram is discussed on the basis of large-N considerations and of the possible analogies and dualities existing with the phase diagram of QCD in presence of an imaginary baryon chemical potential.

Figures (13)

• Figure 1: Polyakov loop susceptibility as a function of $\beta$ on the $40^3 \times 10$ lattice for some explored values of $\theta_L$.
• Figure 2: $R_\theta$ as a function of $1/N_t^2$. The point at $1/N_t = 0$ is the continuum limit extrapolation, assuming $O(a^2)$ corrections.
• Figure 3: Dependence of $\langle\cos(\theta Q)\rangle$ on $\theta$ on the $40^3 \times 10$ lattice and for three different values of $T$.
• Figure 4: Dependence of $\langle\cos(\theta Q)\rangle$ on the number of cooling steps for $T \simeq 1.06\, T_c$ and three values of $\theta$.
• Figure 5: Dependence of the Polyakov loop modulus on $\theta^2$ for $T \simeq 1.055\, T_c$ on the $40^3 \times 10$ lattice. The dashed line is a best fit according to a linear dependence on $\theta^2$.