2021/02/15 by Abu Mohammad Khan
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal field theory #Conformal geometry #Conformal map #Conformal symmetry #Contraction (grammar) #Current algebra #Primary field #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/5.0026059
Accepted for Publication in the Journal of Mathematical Physics
arxiv created 2021/02/15 · openalex created_date 2021/03/01 · openalex publication_date 2021/03/01 · arxiv updated 2021/03/31 · openalex updated_date 2026/08/05
In this paper, we discuss the Inönü–Winger contraction of the conformal algebra. We start with the light-cone form of the Poincaré algebra and extend it to write down the conformal algebra in d dimensions. To contract the conformal algebra, we choose five dimensions for simplicity and compactify the third transverse direction to a circle of radius R following the Kaluza–Klein dimensional reduction method. We identify the inverse radius, 1/R, as the contraction parameter. After the contraction, the resulting representation is found to be the continuous spin representation in four dimensions. Even though the scaling symmetry survives the contraction, the special conformal translation vector changes and behaves like the four-momentum vector. We also discuss the generalization to d dimensions.