Renormalization on the fuzzy sphere

TL;DR

This paper investigates renormalization in scalar field theory on the fuzzy sphere, demonstrating UV cutoff independence and universality at phase boundaries, with behaviors akin to conformal field theories and UV/IR mixing effects.

Contribution

It introduces a numerical approach to renormalization on the fuzzy sphere, showing correlation functions become independent of matrix size through parameter tuning.

Findings

Correlation functions are independent of matrix size after tuning.

Theories on phase boundaries exhibit universal behavior.

Short-distance behavior resembles conformal field theory.

Abstract

We study renormalization on the fuzzy sphere. We numerically simulate a scalar field theory on it, which is described by a Hermitian matrix model. We show that correlation functions defined by using the Berezin symbol are made independent of the matrix size, which is viewed as a UV cutoff, by tuning a parameter of the theory. We also find that the theories on the phase boundary are universal. They behave as a conformal field theory at short distances, while they show an effect of UV/IR mixing at long distances.