Abstract
We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) $$ \mathcal{N}=1,2,4 $$ super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator.
Highlights
The one-loop UV/IR mixing structure of noncommutative N =1 super Yang-Mills theory defined in terms of the noncommutative fields was studied some years ago in a number of papers [1,2,3,4,5]
The outcome was the famous quadratic noncommutative IR divergences which occur in the one-loop gauge field propagator of the non-supersymmetric version of the theory cancel here due to Supersymmetry
The one-loop gauge field propagator still carries a logarithmic UV divergence -a simple pole in Dimensional Regularization- and the dual logarithmic noncommutative IR divergence ln(p2(θp)2) as a result of the UV/IR mixing being at work
Summary
The one-loop UV/IR mixing structure of noncommutative N =1 super Yang-Mills theory defined in terms of the noncommutative fields was studied some years ago in a number of papers [1,2,3,4,5]. The purpose of this paper is to work out all the one-loop 1PI two-point functions, and analyze the UV and noncommutative IR structures of those functions, in noncommutative U(1) N =1,2 and 4 super Yang-Mills theories in the Wess-Zumino gauge, when those theories are defined in terms of ordinary fields by means of the θ-exact Seiberg-Witten maps. The oneloop propagators of the the ordinary fields of noncommutative N =2 and 4 super Yang-Mills U(1) theories defined by using the θ-exact Seiberg-Witten map are worked out in sections 4 and 5 in the ordinary Feynman gauge. Since these supersymmetry transformations generate the noncommutative supersymmetry transformations of (2.2), we conclude that the total θ-exact action (given explicitly in the subsection) has to be invariant up to the second order in e, under the deformed supersymmetry transformations in (2.15)
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