IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and 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.

28+11 pages

References in corpus (17)

• The Lee-Wick Standard Model
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• A translation-invariant renormalizable non-commutative scalar model
• Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture
• Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape
• Emergent Gravity, Matrix Models and UV/IR Mixing
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• Axiomatic formulations of nonlocal and noncommutative field theories
• The Weak Scale from Weak Gravity
• Nonlocal quantum field theory without acausality and nonunitarity at quantum level: is SUSY the key?
• Discrete Gauge Symmetries and the Weak Gravity Conjecture
• Circumventing the No-Go Theorem in Noncommutative Gauge Field Theory
• Translational-invariant noncommutative gauge theory
• Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing
• Noncommutative Time in Quantum Field Theory
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes

Cited by in corpus (5)

• On de Sitter Spacetime and String Theory
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Seiberg-Witten map Invariant Scatterings
• $\mathcal{M}$cTEQ ($\mathcal{M}$ $\mathbf{c}$hiral perturbation theory-compatible deconfinement $\mathbf{T}$emperature and $\mathbf{E}$ntanglement Entropy up to terms $\mathbf{Q}$uartic in curvature) and FM ($\mathbf{F}$lavor $\mathbf{M}$emory)
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories