47 research outputs found
Two-Point Functions on Deformed Spacetime
We present a review of the one-loop photon () and neutrino ()
two-point functions in a covariant and deformed gauge-theory on the
4-dimensional noncommutative spaces, determined by a constant antisymmetric
tensor , and by a parameter-space ,
respectively. For the general fermion-photon and photon
self-interaction the closed form results reveal two-point
functions with all kind of pathological terms: the UV divergence, the quadratic
UV/IR mixing terms as well as a logarithmic IR divergent term of the type
. In addition, the photon-loop produces new tensor
structures satisfying transversality condition by themselves. We show that the
photon two-point function in the 4-dimensional Euclidean spacetime can be
reduced to two finite terms by imposing a specific full rank of
and setting deformation parameters
. In this case the neutrino two-point function
vanishes. Thus for a specific point in the parameter-space
, a covariant -exact approach is able to produce a
divergence-free result for the one-loop quantum corrections, having also both
well-defined commutative limit and point-like limit of an extended object.Comment: review article based on arXiv:0807.4886, arXiv:1109.2485,
arXiv:1111.4951 and arXiv:1306.1239, including some novelt
Quantum duality under the theta-exact Seiberg-Witten map
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.Comment: 47 pages, 21 figures. Version published in JHEP under the reference:
JHEP09(2016)05