# Fixed Point Action and Topology in the CP^3 Model

## TL;DR

This paper introduces a fixed point action for the 2D lattice CP^{N-1} models that reduces cutoff effects and allows for a proper topological charge definition, enabling improved numerical studies of topology.

## Contribution

It defines a classical perfect lattice fixed point action with scale-invariant instantons for CP^{N-1} models, facilitating accurate topological measurements.

## Key findings

- Reduced cutoff effects in simulations
- Proper topological charge without defects
- Studied topological susceptibility in CP^3

## Abstract

We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$ models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cutoff effects in numerical simulations. Furthermore, the action has scale-invariant instanton solutions, which enables us to define a correct topological charge without topological defects. Using a parametrization of the fixed point action for the ${\rm CP}^{3}$ model in a Monte Carlo simulation, we study the topological susceptibility.