Quantum duality under the theta-exact Seiberg-Witten map

Abstract

We show that in the perturbative regime defined by the coupling constant, the theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with or without Supersymmetry-- gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional regularization. We explicitly compute the one-loop two-point function contribution to the on-shell DeWitt effective action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten map. We find that the non-local UV divergences found in the propagator in the Feynman gauge all but disappear, so that they are not physically relevant. We also show that the quadratic noncommutative IR divergences are gauge-fixing independent and go away in the Supersymmetric version of the U(1) theory.

47 pages, 21 figures. Version published in JHEP under the reference: JHEP09(2016)052

References in corpus (3)

• On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
• The Seiberg-Witten map and supersymmetry
• The theta-exact Seiberg-Witten maps at the e3 order