Simulating non-commutative field theory

Abstract

Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present numeric results for 2d NC gauge theory of rank 1, which turns out to be renormalizable. The area law for the Wilson loop holds at small area, but at large area we observe a rotating phase, which corresponds to an Aharonov-Bohm effect. Next we investigate the NC phi^4 model in d=3 and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns.

6 pages, 7 figures, Lattice2002(theoretical)

Cited by in corpus (28)

• SU(N) gauge theories at large N
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• String states, loops and effective actions in noncommutative field theory and matrix models
• Non--Commutative Field Theories beyond Perturbation Theory
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
• 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
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• On the relation between non-commutative field theories at theta = infinity and large N matrix field theories
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• On the Vacuum Cherenkov Radiation in Noncommutative Electrodynamics and the Elusive Effects of Lorentz Violation
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• Spontaneous Symmetry Breaking in Twisted Noncommutative Quantum Theories
• Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory
• Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• Spontaneous symmetry breakdown in fuzzy spheres
• Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories
• Scalar fields in a non-commutative space
• Non-commutative dynamics and roton-like spectra in bosonic and fermionic condensates
• Planar Dominance in Non-commutative Field Theories at Infinite External Momentum
• Inhomogeneous phase of a Gluon Plasma at finite temperature and density