# Correlation functions and renormalization in a scalar field theory on the fuzzy sphere

## TL;DR

This paper investigates the nonperturbative renormalization of a scalar field theory on the fuzzy sphere using matrix models and Monte Carlo simulations, demonstrating independence of correlation functions from the cutoff after tuning.

## Contribution

It introduces a nonperturbative approach to renormalization in fuzzy sphere scalar field theory and shows the theory's potential renormalizability.

## Key findings

- 2-point and 4-point functions become cutoff-independent after tuning
- Correlation functions are nonperturbatively renormalized
- Supports the theory's nonperturbative renormalizability

## Abstract

We study renormalization in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model, where the matrix size plays the role of a UV cutoff. We define correlation functions by using the Berezin symbol identified with a field and calculate them nonperturbatively by Monte Carlo simulation. We find that the 2-point and 4-point functions are made independent of the matrix size by tuning a parameter and performing a wave function renormalization. The results strongly suggest that the theory is nonperturbatively renormalizable in the ordinary sense.