Matrix model approximations of fuzzy scalar field theories and their phase diagrams

Abstract

We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.

v2 minor typos corrected, references updated, version published in JHEP

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Cited by in corpus (8)

• On the quantum structure of space-time, gravity, and higher spin in matrix models
• String states, loops and effective actions in noncommutative field theory and matrix models
• Asymmetric hermitian matrix models and fuzzy field theory
• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Wilsonian Matrix Renormalization Group