Emergent fuzzy geometry and fuzzy physics in $4$ dimensions

Abstract

A detailed Monte Carlo calculation of the phase diagram of bosonic IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are observed with a fluctuation given by a noncommutative $U(1)$ gauge theory very weakly coupled to normal scalar fields. The geometry, which is determined dynamically, is given by the fuzzy spheres ${\mathbf{S}}_N^2$ and ${\mathbf{S}}_N^2\times {\mathbf{S}}_N^2$ respectively. The three and six matrix models are in the same universality class with some differences. For example, in two dimensions the geometry is completely stable, whereas in four dimensions the geometry is stable only in the limit $M⟶\infty$, where $M$ is the mass of the normal fluctuations. The behavior of the eigenvalue distribution in the two theories is also different. We also sketch how we can obtain a stable fuzzy four-sphere ${\mathbf{S}}_N^2\times {\mathbf{S}}_N^2$ in the large $N$ limit for all values of $M$ as well as models of topology change in which the transition between spheres of different dimensions is observed. The stable fuzzy spheres in two and four dimensions act precisely as regulators which is the original goal of fuzzy geometry and fuzzy physics. Fuzzy physics and fuzzy field theory on these spaces are briefly discussed.

arXiv comment45 pages, 18 figures; v2: very minor corrections

References in corpus (37)

• Dielectric-Branes
• Gravity coupled with matter and foundation of non-commutative geometry
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Brane Dynamics in Background Fluxes and Non-commutative Geometry
• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
• Fuzzy CP2
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Finite Gauge Theory on Fuzzy CP^2
• The Fuzzy Ginsparg-Wilson Algebra: A Solution of the Fermion Doubling Problem
• Multi-matrix models and emergent geometry
• A Gauge-Invariant UV-IR Mixing and The Corresponding Phase Transition For U(1) Fields on the Fuzzy Sphere
• Geometry in transition: A model of emergent geometry
• Scalar Field Theory on Fuzzy S^4
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• Stability of fuzzy $S^2\times S^2$ geometry in IIB matrix model
• Matrix Models, Gauge Theory and Emergent Geometry
• Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
• Perturbative dynamics of fuzzy spheres at large N
• Matrix geometries and Matrix Models
• Quantum effective potential for U(1) fields on S^2_L X S^2_L
• Localization for Yang-Mills Theory on the Fuzzy Sphere
• Multi-matrix models at general coupling
• On the Phase Structure of Commuting Matrix Models
• Near commuting multi-matrix models
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $C{P}^3$ as a $S_F^2$ bundle over $S_F^4$
• Fuzzy Nambu-Goldstone Physics
• Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2
• Quantum Equivalence of NC and YM Gauge Theories in 2 D and Matrix Theory
• Towards Noncommutative Fuzzy QED
• Critical Behaviour of the Fuzzy Sphere
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
• Geometry in transition in four dimensions: A model of emergent geometry in the early universe and dark energy
• Duality in Fuzzy Sigma Models
• Nonabelian localization for gauge theory on the fuzzy sphere

Cited by in corpus (2)

• Quantum Gravity as a Multitrace Matrix Model
• Chaos from Equivariant Fields on Fuzzy $S^4$