Quantum duality under the θ-exact Seiberg-Witten map

• Published in: The journal of high energy physics Vol. 2016; no. 9
• Main Authors: Martin, Carmelo P., Trampetic, Josip, You, Jiangyang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 09-09-2016
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; BRST Quantization; Non-Commutative Geometry; Supersymmetric gauge theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2016)052

A
bstract
We show that in the perturbative regime defined by the coupling constant, the
θ
-exact Seiberg-Witten map applied to the 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
θ
-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.