$\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study

TL;DR

This lattice study explores how the topological properties of trace deformed $SU(3)$ Yang-Mills theory depend on the $ heta$ parameter, showing results consistent with standard $SU(3)$ Yang-Mills theory.

Contribution

First numerical lattice investigation of topological susceptibility and $b_2$ coefficient in trace deformed $SU(3)$ Yang-Mills theory across different parameters.

Findings

Topological susceptibility matches standard $SU(3)$ Yang-Mills results.

$b_2$ coefficient results are consistent with the undeformed theory.

Results hold across various lattice spacings and compactification radii.

Abstract

In this paper we investigate, by means of numerical lattice simulations, the topological properties of the trace deformed $SU(3)$ Yang-Mills theory defined on $S_1\times\mathbb{R}^3$. More precisely, we evaluate the topological susceptibility and the $b_2$ coefficient (related to the fourth cumulant of the topological charge distribution) of this theory for different values of the lattice spacing and of the compactification radius. In all the cases we find results in good agreement with the corresponding ones of the standard $SU(3)$ Yang-Mills theory on $\mathbb{R}^4$.