On the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
arXiv:hep-th/0310011 · doi:10.1016/j.nuclphysb.2003.12.010
Abstract
We continue our investigation of the quantum equivalence between commutative and noncommutative Chern-Simons theories by computing the complete set of two-loop quantum corrections to the correlation function of a pure open Wilson line and an open Wilson line with a field strength insertion, on the noncommutative side in a covariant gauge. The conjectured perturbative equivalence between the free commutative theory and the apparently interacting noncommutative one requires that the sum of these corrections vanish, and herein we exhibit the remarkable cancellations that enforce this. From this computation we speculate on the form of a possible all-order result for this simplest nonvanishing correlator of gauge invariant observables.
34 pages, 13 figures; v2: typos fixed (version to appear in NPB)
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- Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
- Maps for currents and anomalies in noncommutative gauge theories
- Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
- Aspects of noncommutativity in field theory, strings and membranes