The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere

TL;DR

This paper uses fuzzy-sphere regularization to study $O(N)$ conformal field theories, providing numerical evidence for operator spectra and correlation functions that match known conformal bootstrap results.

Contribution

It constructs a model realizing $O(N)$ Wilson-Fisher and free-scalar CFTs on the fuzzy sphere for general N, with detailed numerical analysis for N=2,3,4.

Findings

Operator spectra consistent with conformal symmetry

Correlation functions agree with bootstrap results

Numerical evidence supports fuzzy-sphere as a regularization method

Abstract

The fuzzy-sphere regularization is an emerging numerical and theoretical technique for studying conformal field theories (CFTs). In this paper, we apply it to the $O(N)$ vector model, one of the most prominent theories for critical behavior in three space-time dimensions. We construct a model that realizes the $O(N)$ Wilson-Fisher and free-scalar CFTs for general $N$. For $N=2,3,4$, we present numerical evidence including the operator spectra and correlation functions in agreement with conformal symmetry and conformal bootstrap results.