QCD at Fixed Topology

TL;DR

This paper investigates the finite size effects in lattice QCD calculations at fixed topology, providing methods to extract physical results despite topological constraints in numerical simulations.

Contribution

It analytically characterizes finite size effects caused by fixed topology and offers a procedure to recover physical observables from such data.

Findings

Finite size effects are significant at fixed topology.

Methods to extract physical results from fixed topology data.

Analytical expressions for finite size corrections.

Abstract

Since present Monte Carlo algorithms for lattice QCD may become trapped in a fixed topological charge sector, 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.