A matrix phase for the phi^4 scalar field on the fuzzy sphere

Abstract

The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is also one of the simplest examples of a non commutative space to study field theory on. Aside from the usual disordered and uniform phases present in the commutative scalar field theory, we find and discuss in detail a new phase with spontaneously broken rotational invariance, called matrix phase because the geometry of the fuzzy sphere, as expressed by the kinetic term, becomes negligible there. This gives some further insight on the effect of UV-IR mixing, the unusual behaviour which arises naturally when taking the commutative limit of a non commutative field theory.

15 pages, 10 figures. Axes scales of most figures were corrected. Final version

References in corpus (4)

• Stripes from (noncommutative) stars
• Scalar Field Theory on Fuzzy S^4
• On the Origin of the UV-IR Mixing in Noncommutative Matrix Geometry
• A Fuzzy Three Sphere and Fuzzy Tori

Cited by in corpus (35)

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• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Lectures on Matrix Field Theory I
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• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Matrix geometries and Matrix Models
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• Quantum effective potential for U(1) fields on S^2_L X S^2_L
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Emergent geometry from random multitrace matrix models
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Renormalization group approach to matrix models via noncommutative space
• Bootstrapping Fuzzy Scalar Field Theory
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• A Multitrace Approach to Noncommutative Φ_2^4
• Renormalization on the fuzzy sphere
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4
• Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory
• Fuzzy Scalar Field Theory as Matrix Quantum Mechanics
• Phase structure of fuzzy black holes
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• The instability of intersecting fuzzy spheres
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Wilson RG of Noncommutative ${\Phi }_4^4$