Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study

Abstract

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results are consistent with the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either.

28 pages, 15 figures, published version

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• SL(2,R)-Symmetry and Noncommutative Phase Space in (2+2) Dimensions
• A non-perturbative study of non-commutative U(1) gauge theory
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