# Scale Setting and Topological Observables in Pure SU(2) LGT

## TL;DR

This study examines scale setting and topological properties in pure SU(2) lattice gauge theory, demonstrating that cooling scales are efficient and reliable for continuum limit extrapolations and topological measurements.

## Contribution

It introduces the use of cooling scales as an efficient alternative to gradient scales for scale setting and topological analysis in SU(2) LGT, with detailed error estimation.

## Key findings

- Cooling scales show good scaling behavior similar to gradient scales.
- Cooling scales are computationally more efficient than gradient scales.
- Estimated topological susceptibility is $oxed{ ext{approximately }0.643(12) imes T_c^4}$.

## Abstract

In this dissertation, we investigate the approach of pure SU(2) lattice gauge theory to its continuum limit using the deconfinement temperature, six gradient scales, and six cooling scales. We find that cooling scales exhibit similarly good scaling behavior as gradient scales, while being computationally more efficient. In addition, we estimate systematic error in continuum limit extrapolations of scale ratios by comparing standard scaling to asymptotic scaling. Finally we study topological observables in pure SU(2) using cooling to smooth the gauge fields, and investigate the sensitivity of cooling scales to topological charge. We find that large numbers of cooling sweeps lead to metastable charge sectors, without destroying physical instantons, provided the lattice spacing is fine enough and the volume is large enough. Continuum limit estimates of the topological susceptibility are obtained, of which we favor $\chi^{1/4}/T_c = 0.643(12)$. Differences between cooling scales in different topological sectors turn out to be too small to be detectable within our statistical error.