Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry

2005/03/29 by Dominik Stöckinger · 2 citations
Mathematics · Physics and Astronomy · #Action (physics) #Artificial intelligence #Black Holes and Theoretical Physics #Computer science #Dimensional reduction #Dimensional regularization #Effective action #Geometry #Lagrangian #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Reduction (mathematics) #Regularization (linguistics) #Renormalization #Supersymmetry #Theoretical physics #hep-ph

paper · pdf · doi:10.1088/1126-6708/2005/03/076

published as JHEP0503:076,2005 · 19 pages, 4 figures; minor modifications, published in JHEP

openalex publication_date 2005/03/29 · arxiv created 2005/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and elegant relation between the D-dimensional Lagrangian and Ward or Slavnov-Taylor identities, and it can be used in particular to study to what extent dimensional reduction preserves supersymmetry. We give several examples of previously unchecked cases.

Citations

• Scheme dependence and the NSVZ β-function
• N = 1 supersymmetry and the three-loop gauge β-function
• N = 1 supersymmetry and the three-loop anomalous dimension for the chiral superfield
• Regularization dependence of running couplings in softly broken supersymmetry
• Quantum Field - Theory Models in Less Than 4 Dimensions
• Regularization and renormalization of gauge fields

Cited by

• Bare effective potential and Goldstone boson anti-resummation
• N = 4 supersymmetric Yang-Mills thermodynamics to order λ2