Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice

TL;DR

This paper extends a field theoretical approach to compute higher-order terms in the theta expansion of the ground state energy in SU(N) Yang-Mills theories on the lattice, providing new results for SU(3) and insights into ultraviolet fluctuations.

Contribution

It introduces an extended method for calculating higher-order theta terms in lattice Yang-Mills theories and proposes an improved ansatz for better estimates of these terms.

Findings

Determined the fourth order term in the theta expansion for SU(3) pure gauge theory.

Compared results with previous cooling determinations, showing consistency.

Proposed an ansatz that improves estimates of higher-order terms by accounting for ultraviolet fluctuations.

Abstract

We discuss the extension of the field theoretical approach, already used in the lattice determination of the topological susceptibility, to the computation of further terms in the expansion of the ground state energy $F(\theta)$ around $\theta = 0$ in SU(N) Yang-Mills theories. In particular we determine the fourth order term in the expansion for SU(3) pure gauge theory and compare our results with previous cooling determinations. In the last part of the paper we make some considerations about the nature of the ultraviolet fluctuations responsible for the renormalization of the lattice topological charge correlation functions; in particular we propose and test an ansatz which leads to improved estimates of the fourth and higher order terms in the expansion of F(\theta).