On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

Abstract

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.

LaTeX JHEP style, 16 pages, 2 figures

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• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Morita Duality and Noncommutative Wilson Loops in Two Dimensions
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Area preserving diffeomorphisms and Yang-Mills theory in two noncommutative dimensions