# Scaling and Topological Charge of a Fixed Point Action for $SU(2)$ Gauge Theory

## TL;DR

This paper develops an approximate fixed point action for SU(2) gauge theory, performs scaling tests through Monte Carlo simulations, and investigates topological susceptibility and confinement properties across different lattice spacings.

## Contribution

It introduces a new approximate fixed point action for SU(2) gauge theory and demonstrates its scaling behavior and topological properties via comprehensive simulations.

## Key findings

- Topological susceptibility scales with lattice spacing.
- Critical coupling for deconfinement determined for various lattice sizes.
- String tension and heavy quark potential measured consistently across scales.

## Abstract

We construct a few parameter approximate fixed point action for SU(2) pure gauge theory and subject it to scaling tests, via Monte Carlo simulation. We measure the critical coupling for deconfinement for lattices of temporal extent $N_t=2$, 3, 4, the torelon mass at fixed physical volume, and the string tension (and heavy quark potential) from Wilson loops. We calculate the topological susceptibility using inverse blocking and show that it scales over the observed range of lattice spacings.