New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere

Abstract

We propose a new algorithm for simulating noncommutative phi-four theory on the fuzzy sphere based on, i) coupling the scalar field to a U(1) gauge field, in such a way that in the commutative limit N\longrightarrow \infty, the two modes decouple and we are left with pure scalar phi-four on the sphere, and ii) diagonalizing the scalar field by means of a U(N) unitary matrix, and then integrating out the unitary group from the partition function. The number of degrees of freedom in the scalar sector reduces, therefore, from N^2 to the N eigenvalues of the scalar field, whereas the dynamics of the U(1) gauge field, is given by D=3 Yang-Mills matrix model with a Myers term. As an application, the phase diagram, including the triple point, of noncommutative phi-four theory on the fuzzy sphere, is reconstructed with small values of N up to N=10, and large numbers of statistics.

29 pages,9 figures, 4 tables, v2: new section added in which we compare briefly between the different algorithms,30 pages, v3:two figures added, one equation added, various comments added throughout the article, typos corrected, writing style improved, 33 pages

References in corpus (2)

• Finite temperature phase transition of a single scalar field on a fuzzy sphere
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II

Cited by in corpus (16)

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• Second moment fuzzy-field-theory-like matrix models
• Asymmetric hermitian matrix models and fuzzy field theory
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• 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
• Bootstrapping Fuzzy Scalar Field Theory
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• A Multitrace Approach to Noncommutative Φ_2^4
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Eigenvalue-flipping Algorithm for Matrix Monte Carlo