On $\kappa$-Deformation and UV/IR Mixing

TL;DR

This paper investigates UV/IR mixing in a scalar field theory on $ kappa$-deformed space, providing explicit calculations of tadpole diagrams and revealing a distinct form of UV/IR mixing compared to canonical deformation.

Contribution

It offers the first explicit calculation of tadpole diagrams in $ kappa$-deformed space and characterizes the unique UV/IR mixing behavior in this noncommutative setting.

Findings

UV/IR mixing exists in $ kappa$-deformed space.

The UV/IR mixing exhibits a different dressing than in canonical deformation.

Explicit tadpole diagram contributions are calculated.

Abstract

We examine the UV/IR mixing property on a $\kappa$-deformed Euclidean space for a real scalar $\phi^4$ theory. All contributions to the tadpole diagram are explicitly calculated. UV/IR mixing is present, though in a different dressing than in the case of the canonical deformation.