UV/IR mixing in Yang–Mills-type models on Lie-algebraic noncommutative Minkowski spacetimes

Ascertain whether UV/IR mixing occurs in Yang–Mills-type gauge theories constructed on Lie-algebraic noncommutative Minkowski spacetimes—specifically the ρ-Minkowski and κ-Minkowski models defined through twisted derivation-based calculi and actions S_ρ and S_κ—given that one-loop analyses already reveal non-vanishing tadpoles.

Background

The paper constructs Yang–Mills-type gauge theories on newly characterized noncommutative Minkowski spacetimes, focusing on ρ-Minkowski (with unimodular group SE(2)) and κ-Minkowski (non-unimodular affine group). Both models use twisted derivations and gauge-invariant actions adapted to their star-products and involutions.

One-loop studies show non-vanishing tadpoles leading to vacuum instability. However, the presence or absence of UV/IR mixing in these models remains explicitly stated as unknown.