The UV/IR Interplay in Theories with Space-time Varying Non-commutativity

TL;DR

This paper investigates scalar field theories with non-commutativity that varies across space and time, revealing unique UV/IR mixing behaviors and their connection to momentum conservation violations.

Contribution

It introduces the analysis of space-time dependent non-commutativity in scalar field theories and uncovers novel UV/IR mixing structures distinct from constant non-commutative cases.

Findings

UV/IR mixing structure differs from constant non-commutativity cases

UV/IR mixing is linked to momentum conservation violations

New interplay between non-commutativity and UV/IR effects

Abstract

We consider scalar field theory with space and space-time-dependent non-commutativity. In perturbation theory, we find that the structure of the UV/IR mixing is quite different from cases with constant non-commutativity. In particular, UV/IR mixing becomes intertwined in an interesting way with violations of momentum conservation.