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Calculating the Higgs mass in string theory

Abel, Steven; Dienes, Keith R.

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Keith R. Dienes


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 world sheet 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 effective field theory (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 scaleinversion 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.


Abel, S., & Dienes, K. R. (2021). Calculating the Higgs mass in string theory. Physical Review D, 104(12),

Journal Article Type Article
Acceptance Date Dec 2, 2021
Online Publication Date Dec 29, 2021
Publication Date 2021
Deposit Date Feb 22, 2022
Publicly Available Date Feb 22, 2022
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 104
Issue 12


Published Journal Article (1.5 Mb)

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Copyright Statement
Published by the American Physical Society under the terms of<br /> the Creative Commons Attribution 4.0 International license.<br /> Further distribution of this work must maintain attribution to<br /> the author(s) and the published article&rsquo;s title, journal citation,<br /> and DOI. Funded by SCOAP3.

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