# Instantons and Fixed Point Actions in SU(2) Gauge Theory

## TL;DR

This paper investigates instantons in SU(2) lattice gauge theory using fixed point actions, proposing a method to measure topological charge and demonstrating that smooth configurations' action aligns with continuum values.

## Contribution

It introduces a consistent inverse renormalization group method for topological charge measurement and analyzes instanton properties with fixed point actions.

## Key findings

- Action of smooth configurations ≥ continuum value 8π²/g²
- Proposes a new method for topological charge measurement
- Analyzes instanton properties in lattice gauge theory

## Abstract

We describe the properties of instantons in lattice gauge theory when the action is a fixed point action of some renormalization group transformation. We present a theoretically consistent method for measuring topological charge using an inverse renormalization group transformation. We show that, using a fixed point action, the action of smooth configurations with non-zero topological charge is greater than or equal to its continuum value $8\pi^2/g^2$.