Combining ordinary and topological finite volume effects for fixed topology simulations

TL;DR

This paper extends the understanding of finite volume effects in lattice quantum field theories by combining topological and ordinary finite size effects, providing a method to extract physical results from simulations with fixed topology.

Contribution

It introduces an extended relation that accounts for both topological and ordinary finite volume effects in lattice simulations, improving the accuracy of physical predictions.

Findings

Numerical results for SU(2) Yang-Mills theory demonstrate the method's effectiveness.

The extended relation helps correct finite volume effects in fixed topology simulations.

The approach enhances the reliability of lattice QCD calculations at fine lattice spacings.

Abstract

In lattice quantum field theories with topological sectors, simulations at fine lattice spacings --- with typical algorithms --- tend to freeze topologically. In such cases, specific topological finite size effects have to be taken into account to obtain physical results, which correspond to infinite volume or unfixed topology. Moreover, when a theory like QCD is simulated in a moderate volume, one also has to overcome ordinary finite volume effects (not related to topology freezing). To extract physical results from simulations affected by both types of finite volume effects, we extend a known relation between hadron masses at fixed and unfixed topology by additionally incorporating ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.