Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces

Abstract

We present non-perturbative results for U(1) gauge theory in spaces, which include a non-commutative plane. In contrast to the commutative space, such gauge theories involve a Yang-Mills term, and the Wilson loop is complex on the non-perturbative level. We first consider the 2d case: small Wilson loops follows an area law, whereas for large Wilson loops the complex phase rises linearly with the area. In four dimensions the behavior is qualitatively similar for loops in the non-commutative plane, whereas the loops in other planes follow closely the commutative pattern. In d=2 our results can be extrapolated safely to the continuum limit, and in d=4 we report on recent progress towards this goal.

arXiv comment9 pages, 7 figures, talk presented at "Ahrenshoop 2004"

References in corpus (23)

• String Theory and Noncommutative Geometry
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Noncommutative Yang-Mills in IIB Matrix Model
• Wilson Loops in Noncommutative Yang Mills
• Finite N Matrix Models of Noncommutative Gauge Theory
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Phase structure of non-commutative scalar field theories
• Stripes from (noncommutative) stars
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• Instability of Non-Commutative SYM Theories at Finite Temperature
• Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
• Nonuniform symmetry breaking in noncommutative $\lambda {\Phi }^4$ theory
• Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory
• Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
• 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
• Numerical Study of the Double Scaling Limit in Two-Dimensional Large N Reduced Model
• Wilson line correlators in two-dimensional noncommutative Yang-Mills theory
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

Cited by in corpus (19)

• 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
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• Lectures on Matrix Field Theory I
• Noncommutative QFT and Renormalization
• 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
• Morita Duality and Noncommutative Wilson Loops in Two Dimensions
• On The Bound States Of Photons In Noncommutative Quantum Electrodynamics
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions
• Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
• Noncommutative Fluids
• Noncommutative Two-Dimensional Gauge Theories
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons