Non--Commutative Field Theories beyond Perturbation Theory

Abstract

We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm effect if we identify θ= 1/B. Next we study the 3d λϕ^{4} model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjorn and Catterall that such stripes occur even in d=2, although they imply the spontaneous breaking of translation symmetry. However, in d=3 and d=2 we observe only patterns of two stripes to be stable in the range of parameters investigated.

8 pages, 8 figures, talk presented at 35th Ahrenshoop Symposium

References in corpus (20)

• String Theory and Noncommutative Geometry
• Noncommutative Perturbative Dynamics
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Space/Time Non-Commutativity and Causality
• Wilson Loops in Noncommutative Yang Mills
• On the unitarity problem in space/time noncommutative theories
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Finite N Matrix Models of Noncommutative Gauge Theory
• Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
• Phase structure of non-commutative scalar field theories
• Stripes from (noncommutative) stars
• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• Noncommutative Field Theory and Spontaneous Symmetry Breaking
• Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime
• Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory
• Simulating non-commutative field theory
• Fuzzy Sphere from Matrix Model
• UV/IR mixing and the Goldstone theorem in noncommutative field theory
• Validity of Goldstone Theorem at Two Loops in Noncommutative U(N) Linear Sigma Model

Cited by in corpus (20)

• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• 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
• Nonuniform symmetry breaking in noncommutative $\lambda {\Phi }^4$ theory
• The Fuzzy Disc
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• On the relation between non-commutative field theories at theta = infinity and large N matrix field theories
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• On the Vacuum Cherenkov Radiation in Noncommutative Electrodynamics and the Elusive Effects of Lorentz Violation
• Numerical results on the Non-commutative λϕ^4 Model
• A New Matrix Model for Noncommutative Field Theory
• Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories
• Lattice Superstring and Noncommutative Geometry
• Non-commutative dynamics and roton-like spectra in bosonic and fermionic condensates
• Effective Potential and Spontaneous Symmetry Breaking in the Noncommutative phi^6 Model
• Inhomogeneous phase of a Gluon Plasma at finite temperature and density