Effective action and phase transitions of scalar field on the fuzzy sphere

Abstract

Scalar field theory on the fuzzy two-sphere, represented as a hermitian matrix model that includes kinetic, mass and quartic interaction terms, is studied. The effective action in the symmetric large-N regime is analyzed using a self-consistent bootstrap method which fixes its form up to sixth order in the eigenvalues and gives a closed expression to all orders in the quadratic invariant of the matrix, valid close to semicircular distributions. Using this action the eigenvalue distribution is calculated for the interacting theory in the appropriate scaling limit and the phase transition from the disordered to the symmetric ordered phase is identified, including nonperturbative effects.

Version to appear in Physical Review D

References in corpus (3)

• Physics and Mathematics of Calogero particles
• The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CP^n
• Random matrix approach to scalar fields on fuzzy spaces

Cited by in corpus (24)

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• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Emergent geometry from random multitrace matrix models
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• A Multitrace Approach to Noncommutative Φ_2^4
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Renormalization on the fuzzy sphere
• Approximate treatment of noncommutative curvature in quartic matrix model
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Conserved symmetries in noncommutative quantum mechanics
• Quantized Noncommutative Geometry from Multitrace Matrix Models
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• The multitrace matrix model: An alternative to Connes NCG and IKKT model
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• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Fuzzy field theories and related matrix models
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime