Quantum duality under the theta-exact Seiberg-Witten map
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2016
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Springer
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Abstract
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.
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© The Authors. The work by C.P. Martín has been financially supported in part by the Spanish MINECO through grant FPA2014-54154-P. J.Y. has been fully supported by Croatian Science Foundation under Project No. IP-2014-09-9582. The work J.T. is conducted under the European Commission and the Croatian Ministry of Science, Education and Sports Co-Financing Agreement No. 291823. In particular, J.T. acknowledges project financing by the Marie Curie FP7-PEOPLE-2011-COFUND program NEWFELPRO: Grant Agreement No. 69, and Max-Planck-Institute for Physics, and W. Hollik for hospitality. We would like to acknowledge L. Álvarez-Gaume, J. Ellis and P. Minkowski for fruitful discussions and CERN Theory Division, where part of this work was conducted, for hospitality. We would also like to thank J. Erdmenger and W. Hollik, for fruitful discussions. J.Y. would like to acknowledge the Center of Theoretical Physics, College of Physical Science and Technology, Sichuan University, China, for hospitality during his visit, as well as Yan He, Xiao Liu, Hiroaki Nakajima, Bo Ning, Rakibur Rahman, Zheng Sun, Peng Wang, Houwen Wu, Haitang Yang and Shuxuan Ying for fruitful discussions. J.Y. would also like to acknowledge H2020 CSA Twinning project No. 692194, “RBI-T-WINNING” for financially supporting his trip to Max-Planck-Institute for Physics, Munich, Germany and CERN. A great deal of computation was done by using MATHEMATICA 8.0 [36] plus the tensor algebra package xACT [37]. Special thanks to A. Ilakovac and D. Kekez for the computer software and hardware support.