Topological susceptibility near $T_{c}$ in SU(3) gauge theory

TL;DR

This study investigates the behavior of topological susceptibility in SU(3) gauge theory at finite temperature, revealing a rapid decline near the phase transition and supporting the diluted instanton gas model at high temperatures.

Contribution

It provides new lattice QCD results on topological susceptibility and cumulants near the critical temperature using anisotropic lattices and improved smoothing techniques.

Findings

Topological susceptibility decreases sharply near $T_c$.

Topological excitations persist well above $T_c$.

High-temperature ratio matches instanton gas predictions.

Abstract

Topological charge susceptibility $\chi_{t}$ for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for $\chi_{t}$ with values decreasing from $(188(1)\mathrm{MeV})^{4}$ to $(67(3)\mathrm{MeV})^{4}$ as the temperature increased from zero temperature to $1.9T_{c}$ which demonstrates the existence of topological excitations far above $T_{c}$. The 4th order cumulant $c_4$ of topological charge, as well as the ratio $c_4/\chi_t$ are also investigated. Results of $c_4$ show step-like behavior near $T_c$ while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.