# A New Lattice Action for Studying Topological Charge

## TL;DR

This paper introduces a new lattice action for non-abelian gauge theories that reduces artifacts in topological charge calculations by interpolating fields to a finer lattice, improving continuum limit behavior.

## Contribution

It proposes a novel lattice action using gauge covariant interpolation to minimize artifacts in topological susceptibility computations.

## Key findings

- Finer lattice interpolations satisfy the continuum bound for topological charge.
- Numerical analysis in the $O(3)$ sigma-model shows halving lattice spacing suffices.
- The new approach improves the accuracy of topological charge measurements.

## Abstract

We propose a new lattice action for non-abelian gauge theories, which will reduce short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. If the latter is fine enough, the action of all configurations with non-zero topological charge will satisfy the continuum bound. As a simpler example we consider the $O(3)$ $\sigma$-model in two dimensions, where a numerical analysis of discretized continuum instantons indicates that a finer lattice with half the lattice spacing of the original is enough to satisfy the continuum bound.