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

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.

22 pages, 11 figures, published version

References in corpus (2)

• Finite temperature phase transition of a single scalar field on a fuzzy sphere
• Random matrix approach to scalar fields on fuzzy spaces

Cited by in corpus (4)

• Asymmetric hermitian matrix models and fuzzy field theory
• Renormalization on the fuzzy sphere
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type