Calculating the Higgs Mass in String Theory

TL;DR

This paper develops a string-theoretic method to calculate one-loop Higgs masses applicable to all closed string models, revealing a connection between the Higgs mass and the cosmological constant, and exploring scale-inversion duality in the Higgs sector.

Contribution

It introduces a universal string framework for Higgs mass calculation that does not rely on specific model assumptions and relates Higgs mass to the cosmological constant.

Findings

Higgs mass is generically related to the one-loop cosmological constant via a gravitational modular anomaly.

A scale-inversion duality symmetry affects the running of the Higgs mass at high energies.

A stringy effective potential for Higgs fields is identified.

Abstract

In this paper, we establish a fully string-theoretic framework for calculating one-loop Higgs masses directly from first principles in perturbative closed string theories. Our framework makes no assumptions other than worldsheet modular invariance and is therefore applicable to all closed strings, regardless of the specific string construction utilized. This framework can also be employed even when spacetime supersymmetry is broken (and even when this breaking occurs at the Planck scale), and can be utilized for all scalar Higgs fields, regardless of the particular gauge symmetries they break. This therefore includes the Higgs field responsible for electroweak symmetry breaking in the Standard Model. Notably, using our framework, we demonstrate that a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, thereby yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. We also discuss a number of crucial issues involving the use and interpretation of regulators in UV/IR-mixed theories such as string theory, and the manner in which one can extract an EFT description from such theories. Finally, we analyze the running of the Higgs mass within such an EFT description, and uncover the existence of a "dual IR" region which emerges at high energies as the consequence of an intriguing scale-inversion duality symmetry. We also identify a generic stringy effective potential for the Higgs fields in such theories. Our results can therefore serve as the launching point for a rigorous investigation of gauge hierarchy problems in string theory.