Abstract
We consider a family of κ-Poincaré invariant scalar field theories on 4-d κ-Minkowski space with quartic orientable interaction, that is for which ϕ and its conjugate ϕ† alternate in the quartic interaction, and whose kinetic operator is the square of a Uκ(iso(4))-equivariant Dirac operator. The formal commutative limit yields the standard complex ϕ4 theory. We find that the 2-point function receives UV linearly diverging 1-loop corrections while it stays free of IR singularities that would signal occurrence of UV/IR mixing. We find that all the 1-loop planar and non-planar contributions to the 4-point function are UV finite, stemming from the existence of the particular estimate for the propagator partly combined with its decay properties at large momenta, implying formally vanishing of the beta-functions at 1-loop so that the coupling constants stay scale-invariant at 1-loop.
Highlights
JHEP01(2019)064 of quantum groups [8, 9] as well as twists deformations, have been widely explored resulting in a huge literature on the subject
We find that the 2-point function receives UV linearly diverging 1-loop corrections while it stays free of IR singularities that would signal occurrence of UV/IR mixing
It turns out that the requirement of κ-Poincare invariance implies that the (Lebesgue) integral contained in the action functional behaves as a twisted trace with respect to the star product, defining a KMS weight [46, 47] on the algebra modeling the κ-Minkowski space which may be viewed as the property replacing the usual cyclicity of the trace in the action functional
Summary
Zκ[J, J ] := dφdφ e−Sκkin(φ,φ)−Sκint(φ,φ)+ d4x J(x)φ(x)+ d4x J(x)φ(x). is the generating functional of connected correlation functions for the free field theory in which Pκ(p) is the propagator, i.e. Recalling that the deformed translation Hopf subalgebra of Pκ is generated by Pμ and E, it is natural to interpret y as related to the “physical” quantity replacing the time-like momenta, says q0, in the NCFT This is in some sense apparent by considering the term. Assuming |q0| ≤ M (Λ0), one finds κ We will use the latter condition to regularize the y-integrals appearing in the computation of the 2- and 4-point functions. When g1 = g2, it can be realized from (3.27) that ω1 = ω2 so that the quadratic mass term becomes stable against (1-loop) radiative corrections This reflects the fact that the classical action functional (2.1)–(2.4) becomes invariant under the symmetry φ → φ†, φ† → φ.
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