Elimination of IR/UV via Gravity in Noncommutative Field Theory

TL;DR

Coupling noncommutative geometry to gravity can eliminate the IR/UV mixing problem in particle physics models, potentially leading to new cosmological insights.

Contribution

This paper demonstrates how coupling NCG to gravity modifies the theory to resolve the IR/UV problem.

Findings

IR/UV problem is mitigated by gravity coupling

Propagator modifications depend on NCG and metric variation

Potential cosmological implications of anti-symmetric metric components

Abstract

Models of particle physics with Noncommutative Geometry (NCG) generally suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known as the "IR/UV Problem" which would tend to compromise their phenomenological relevance. In this Letter we explicitly show how one may remedy this by coupling NCG to gravity. In the simplest scenario the Lagrangian gets multiplied by a nonconstant background metric; in $\phi-4$ theory the theorem that $\int d^4 x \phi \star \phi = \int d^4 x \phi^2$ is no longer true and the field propagator gets modified by a factor which depends on both NCG and the variation of the metric. A suitable limit of this factor as the propagating momentum gets asymptotically large then eradicates the IR/UV problem. With gravity and NCG coupled to each other, one might expect anti-symmetric components to arise in the metric. Cosmological implications of such are subsequently discussed.