Mass corrections in string theory and lattice field theory

TL;DR

This paper investigates quantum mass corrections to scalar fields in Kaluza-Klein compactifications, demonstrating their universality across string and lattice UV completions and exploring suppression mechanisms in supersymmetric theories.

Contribution

It provides a comparative analysis of mass corrections in string and lattice frameworks, confirming their universality and examining suppression effects in supersymmetric models.

Findings

Mass corrections are UV-scale independent in the large radius limit.

Universality of mass corrections holds across different UV completions.

Supersymmetric theories exhibit suppressed scalar masses due to gauge invariance and fermion-boson degeneracy.

Abstract

Kaluza-Klein compactifications of higher dimensional Yang-Mills theories contain a number of four dimensional scalars corresponding to the internal components of the gauge field. While at tree-level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1-loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK--modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius $R$ is much bigger than the scale of the UV completion ($R \gg \sqrt{\alpha'},a$), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in $\mathcal N=2,4$ Super Yang-Mills is highly suppressed due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.