A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane

Abstract

We perform a non-perturbative study of pure gauge theory in a two dimensional non-commutative (NC) space. On the lattice, it is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large-N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. Based on a Morita equivalence, the large-N double scaling limit corresponds to the continuum limit of NC gauge theory, so the observed large-N scaling demonstrates the non-perturbative renormalizability of this NC field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter.

18 pages, 6 figures, final version published in JHEP

References in corpus (35)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Perturbative Dynamics
• D-branes and the Noncommutative Torus
• Noncommutative Yang-Mills in IIB Matrix Model
• Wilson Loops in Noncommutative Yang Mills
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Morita equivalence and duality
• Finite N Matrix Models of Noncommutative Gauge Theory
• Nonperturbative Dynamics of Noncommutative Gauge Theory
• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Phase structure of non-commutative scalar field theories
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• Non-renormalizability of θ-expanded noncommutative QED
• Gauge Theory on a Quantum Phase Space
• Open Wilson Lines in Noncommutative Gauge Theory and Tomography of Holographic Dual Supergravity
• A Consistent Noncommutative Field Theory: the Wess-Zumino Model
• Non-Commutative Geometry on a Discrete Periodic Lattice and Gauge Theory
• The Quantum Hall Effect: Novel Excitations and Broken Symmetries
• Wilsonian Renormalization Group and the Non-Commutative IR/UV Connection
• Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance
• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• Towards the solution of noncommutative $Y{M}_2$: Morita equivalence and large N-limit
• Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory
• On the UV renormalizability of noncommutative field theories
• Numerical Study of the Double Scaling Limit in Two-Dimensional Large N Reduced Model
• On Existence of Nontrivial Fixed Points in Large $N$ Gauge Theory in More than Four Dimensions
• On the Hierarchy Between Non-Commutative and Ordinary Supersymmetric Yang-Mills
• Hard Non-commutative Loops Resummation
• Flux noise in high-temperature superconductors
• Twisted Eguchi-Kawai Reduced Chiral Models
• The Area Law in Matrix Models for Large N QCD Strings
• Loop Equation and Wilson line Correlators in Non-commutative Gauge Theories

Cited by in corpus (51)

• SU(N) gauge theories at large N
• 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
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
• 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
• Supersymetry on the Noncommutative Lattice
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces
• Perturbative dynamics of fuzzy spheres at large N
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions
• Scaling properties of the perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory
• Non--Commutative Field Theories beyond Perturbation Theory
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• 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
• Lectures on Two-Dimensional Noncommutative Gauge Theory 2: Quantization
• Volume independence for Yang-Mills fields on the twisted torus
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• Morita Duality and Noncommutative Wilson Loops in Two Dimensions
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
• On The Bound States Of Photons In Noncommutative Quantum Electrodynamics
• 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
• Hamilton-Jacobi Method and Effective Actions of D-brane and M-brane in Supergravity
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• Matrix Models
• On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Probability of the Standard Model Appearance from a Matrix Model
• Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
• Towards Noncommutative Fuzzy QED
• First Simulation Results for the Photon in a Non-Commutative Space
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Lattice Superstring and Noncommutative Geometry
• The instability of intersecting fuzzy spheres
• Could the photon dispersion relation be non-linear ?
• Non-commutative Field Theory on S^4
• The Photon Dispersion as an Indicator for New Physics ?