2008/12/31 by Luigi Del Debbio, Eoin Kerrane, Rodolfo Russo · 13 citations
Mathematics · Physics and Astronomy · #Background field method #Black Holes and Theoretical Physics #Compactification (mathematics) #Effective field theory #Gauge theory #Lattice (music) #Lattice field theory #Mass gap #Massless particle #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Quantum mechanics #Regularization (linguistics) #Renormalization #Scalar field #Theoretical physics #Yang–Mills theory #hep-th
paper · pdf · open access · doi:10.1103/physrevd.80.025003
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 80(2) (American Physical Society) · 27 pages
openalex publication_date 2009/07/06 · arxiv created 2009/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Kaluza-Klein (KK) compactifications of higher-dimensional Yang-Mills theories contain a number of 4-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\ensuremath≫√\ensuremathα^\ensuremath', 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 N=2, 4 super Yang-Mills is highly suppressed, even if the lattice regularization breaks all supersymmetries explicitly. This is due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.