Topological susceptibility at zero and finite $T$ in SU(3) Yang-Mills theory

TL;DR

The paper tackles the topological susceptibility $\chi$ in pure $SU(3)$ Yang–Mills theory at zero and finite temperature, in the framework of the $U_A(1)$ anomaly and its temperature dependence across the deconfinement transition. It introduces an improved lattice topological charge density operator with smearing to suppress artefacts and performs non-perturbative renormalization of the lattice measurements via $Z^{(i)}(\beta)$ and $M^{(i)}(\beta)$ by heating techniques and flat-configurations. The study yields a precise zero-temperature determination of $\chi$ consistent with the Witten– Veneziano relation and shows that $\chi$ drops to near zero at the deconfinement temperature $T_c$, substantiating the suppression of topological fluctuations in the high-temperature phase. The approach demonstrates significant reduction of lattice artefacts and provides robust finite-temperature insights into topological properties of non-Abelian gauge theories.

Abstract

We determine the topological susceptibility $χ$ at T=0 in pure SU(3) gauge theory and its behaviour at finite $T$ across the deconfining transition. We use an improved topological charge density operator. $χ$ drops sharply by one order of magnitude at the deconfining temperature $T_c$.

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