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- TL;DR Summary
- based on UV-IR duality; similarities to Veltman condition

https://arxiv.org/abs/2106.04622

Steven Abel, Keith R. Dienes

**Calculating the Higgs Mass in String Theory**Steven Abel, Keith R. Dienes

*[Submitted on 8 Jun 2021]*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.

There are at least two properties of the Higgs mass one might hope to explain with such a fundamental calculation: its criticality, and its participation in the Veltman-like sum rule discovered by Lopez-Castro and Pestieau. Veltman's condition does rate a mention (after 6.11), and the running of the Higgs mass is discussed (figure 3, page 37), but at first glance the formulas look too complicated. On the other hand, the role of the supertrace is very promising - the supertrace is ideal for creating Veltman-like relations - and we are told directly (end of page 54) that "in string theory... the supertraces... are evaluated over theNotably, 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.

*entire*spectrum of string states and not merely the light states within the EFT". The LC&P sum rule deviates from the Veltman condition; perhaps this is a clue for how to embed it in string theory.