Wolfgang Bietenholz (Zeuthen):
Simulating U(1) Gauge Theory on NonCommutative Spaces
Abstract:
We first present a nonperturbative study of
the φ^{4} model on a three dimensional noncommutative space, based on
numerical simulations. If the extent of noncommutativity exceeds a lower limit, a
new phase occurs where translation symmetry is spontaneously broken, so that stripe
patterns dominate. In this phase the dispersion relation is deformed in the infrared
regime, in agreement with the property of UV/IR mixing. Next we address noncommutative
U(1) gauge theory. Here the Wilson loop is complex on the nonperturbative level.
We first consider the 2d case: small Wilson loops are almost real and follow an area law,
whereas for large Wilson loops the complex phase rises linearly with the area,
analogous to the AharonovBohm effect. In d=4 the behaviour is qualitatively
similar for loops in the noncommutative plane, whereas the loops in other planes
follow closely the commutative pattern. In both cases we also discuss the extrapolation
of our results to the continuum and infinite volume by means of a double scaling limit.
The 4d phase diagram reveals that the photon may survive in a noncommutative world,
despite the perturbatively negative IR singularity, and its dispersion relation could
be confronted with experimental data in the near future.
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