$\kappa$-Poincar\'e invariant orientable field theories at 1-loop

TL;DR

This paper studies a family of $$-Poincaré invariant scalar field theories on 4D $$-Minkowski space, analyzing their 1-loop quantum corrections and showing UV finiteness of 4-point functions and scale invariance at 1-loop.

Contribution

It introduces a new class of $$-Poincaré invariant scalar theories with orientable interactions and demonstrates their UV properties and scale invariance at 1-loop.

Findings

2-point function has UV linear divergence at 1-loop

4-point functions are UV finite at 1-loop

Beta-functions vanish at 1-loop, indicating scale invariance

Abstract

We consider a family of $\kappa$-Poincar\'e invariant scalar field theories on 4-d $\kappa$-Minkowski space with quartic orientable interaction, that is for which $\phi$ and its conjugate $\phi^\dag$ alternate in the quartic interaction, and whose kinetic operator is the square of a $U_\kappa(iso(4))$-equivariant Dirac operator. The formal commutative limit yields the standard complex $\phi^4$ 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.