  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.
