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.

Highlights

  • Extracting phenomenological predictions from string theory is a subtle task

  • A central question when analyzing any string theory is to understand the properties of its ubiquitous scalars—its Higgs fields, its moduli fields, its axions, and so forth

  • Our framework can be applied at all energy scales, is independent of any supersymmetry, and maintains world sheet modular invariance and finiteness at all times

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Summary

INTRODUCTION

Extracting phenomenological predictions from string theory is a subtle task. Chief among the complications is the question of finding a suitable vacuum. IV, we shall use these modular-invariant regulators in order to recast our results for the Higgs mass in a form that is closer to what we might expect in field theory This will allow us to develop an understanding of how the Higgs mass “runs” in string theory and to develop a physical “renormalization” prescription that can operate at all scales. It is this extra ingredient which is critical for ensuring consistency with the underlying string symmetries, and which allows us to probe the unique effects of such symmetries (such as those induced by UV/IR mixing) in a rigorous manner

A GENERAL FRAMEWORK
Preliminaries
N g ðτÞf ðτÞ
Higgsing and charge-lattice deformations
Example
Calculating the Higgs mass
Modular completion and additional Higgs-mass contributions
Classical stability condition
A relation between the Higgs mass and the cosmological constant
REGULATING THE HIGGS MASS
The Rankin-Selberg technique
Regulating divergences
Minimal regulator
Nonminimal regulators
Modular-invariant regulators
Aligning the nonminimal and modular-invariant regulators
TOWARD A FIELD-THEORETIC INTERPRETATION
Modular invariance, UV/IR equivalence, and the passage to an EFT
The divergence structure of the Higgs mass
Results using the minimal regulator
Results using the nonminimal regulator
Results using the modular-invariant regulator
Contribution from the cosmological constant
The Higgs mass in string theory
TRANSCENDING THE CHARGE LATTICE
X ’s without Q’s: A reformulation of the partition-function insertions
A stringy effective potential for the Higgs
24 M2StrM2
PULLING IT ALL TOGETHER
Z d22τ
Full Text
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