A New Non-Renormalization Theorem from UV/IR Mixing

TL;DR

This paper proves a new non-renormalization theorem stemming from UV/IR mixing in string theories, showing that certain physical quantities do not run with energy scale and instead reach a fixed point, independent of supersymmetry.

Contribution

It introduces a novel non-renormalization theorem derived from UV/IR mixing applicable to a broad class of string theories, impacting phenomenological predictions.

Findings

Certain physical quantities do not exhibit logarithmic or power-law running.

Theories enter an effective fixed-point regime above the compactification scale.

UV/IR mixing can resolve hierarchy problems without supersymmetry.

Abstract

In this paper, we prove a new non-renormalization theorem which arises from UV/IR mixing. This theorem and its corollaries are relevant for all four-dimensional tachyon-free closed string theories which can be realized from higher-dimensional theories via geometric compactifications. As such, they therefore apply regardless of the presence or absence of spacetime supersymmetry and regardless of the gauge symmetries or matter content involved. This theorem resolves a hidden clash between modular invariance and the process of decompactification, and enables us to uncover a number of surprising phenomenological properties of these theories. Chief among these is the fact that certain physical quantities within such theories cannot exhibit logarithmic or power-law running and instead enter an effective fixed-point regime above the compactification scale. This cessation of running occurs as the result of the UV/IR mixing inherent in the theory. These effects apply not only for gauge couplings but also for the Higgs mass and other quantities of phenomenological interest, thereby eliminating the logarithmic and/or power-law running that might have otherwise appeared for such quantities. These results illustrate the power of UV/IR mixing to tame divergences -- even without supersymmetry -- and reinforce the notion that UV/IR mixing may play a vital role in resolving hierarchy problems without supersymmetry.