Renormalization on the fuzzy sphere

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.

arXiv comment19 pages, 12 figures, minor changes

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Cited by in corpus (6)

• Second moment fuzzy-field-theory-like matrix models
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Laplacians on Fuzzy Riemann Surfaces
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• 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