IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem

TL;DR

This paper investigates how UV/IR mixing in noncommutative field theories can lead to emergent infrared scales from ultraviolet physics, offering insights into the hierarchy problem and the limitations of effective field theories.

Contribution

It analyzes UV/IR mixing in noncommutative field theories, especially Yukawa and Wess-Zumino models, revealing new infrared poles and the interplay with UV-finiteness.

Findings

Identification of a new infrared pole in Yukawa theory.

Demonstration of UV/IR mixing effects in noncommutative Wess-Zumino model.

Insights into the limitations of noncommutative theories for addressing the hierarchy problem.

Abstract

The persistence of the hierarchy problem points to a violation of effective field theory expectations. A compelling possibility is that this results from a physical breakdown of EFT, which may arise from correlations between ultraviolet (UV) and infrared (IR) physics. To this end, we study noncommutative field theory (NCFT) as a toy model of UV/IR mixing which generates an emergent infrared scale from ultraviolet dynamics. We explore the range of such theories where ultraviolet divergences are transmogrified into infrared scales, focusing particularly on the properties of Yukawa theory, where we identify a new infrared pole accessible in the $s$-channel of the Lorentzian theory. We further investigate the interplay between UV-finiteness and UV/IR mixing by studying properties of the softly-broken noncommutative Wess-Zumino model as soft terms are varied relative to the cutoff. While the Lorentz violation inherent to noncommutative theories may limit their direct application to the hierarchy problem, these toy models provide general lessons to guide the realization of UV/IR mixing in more realistic theories.