Physical Observables from Lattice QCD at Fixed Topology

TL;DR

This paper investigates the finite size effects in lattice QCD calculations performed at fixed topological charge, providing methods to extract physical observables despite topological trapping in simulations.

Contribution

It derives the finite size effects caused by fixed topology and offers a way to obtain physical results from such lattice QCD data.

Findings

Finite size effects are characterized and calculable.

Methods to extract physical observables from fixed topology data.

Fixed topology effects vanish in the infinite volume limit.

Abstract

Because present Monte Carol algorithms for lattice QCD may become trapped in a given topological charge sector when one approaches the continuum limit, it is important to understand the effect of calculating at fixed topology. In this work, we show that although the restriction to a fixed topological sector becomes irrelevant in the infinite volume limit, it gives rise to characteristic finite size effects due to contributions from all $\theta$-vacua. We calculate these effects and show how to extract physical results from numerical data obtained at fixed topology.