# Scaling topological charge in the CP^3 model using a fixed point action

## TL;DR

This paper introduces a fixed point action for the 2D lattice CP^{N-1} models, reducing cut-off effects and enabling precise topological charge measurement through scale-invariant instanton solutions, with results demonstrated in CP^3.

## Contribution

It presents a classical perfect lattice fixed point action for CP^{N-1} models that minimizes discretization errors and allows topological charge evaluation without defects.

## Key findings

- Reduced cut-off effects in numerical simulations.
- Successful scaling of topological susceptibility in CP^3.
- Scale-invariant instanton solutions enable defect-free topological charge measurement.

## Abstract

We define a fixed point action in two-dimensional lattice CP^{N-1} models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cut-off effects in numerical simulations. Furthermore, the action has scale invariant instanton solutions, which enables us to define a topological charge without topological defects. We present results for the scaling of the topological suceptibility from a Monte Carlo simulation in the CP^3 model.