2019/08/31 by Athanasios Chatzistavrakidis, Georgios Karagiannis, Peter Schupp
Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dual polyhedron #Gauge theory #Generality #Graviton #Noncommutative and Quantum Gravity Theories #Standard Model (mathematical formulation) #Tensor (intrinsic definition) #Tensor field #Unified field theory #hep-th
paper · pdf · doi:10.1007/s00220-020-03728-x
47 pages; version 3: Minor update in the references list. Commun. Math. Phys. (2020)
openalex created_date 2019/09/05 · openalex publication_date 2020/03/18 · arxiv created 2020/12/01 · arxiv updated 2020/12/02 · openalex updated_date 2026/08/05
Gauge theories can often be formulated in different but physically equivalent ways, a concept referred to as duality. Using a formalism based on graded geometry, we provide a unified treatment of all parent theories for different types of standard and exotic dualizations. Our approach is based on treating tensor fields as functions of a certain degree on graded supermanifolds equipped with a suitable number of odd coordinates. We present a universal two-parameter first order action for standard and exotic electric/magnetic dualizations and prove in full generality that it yields two dual second order theories with the desired field content and dynamics. Upon choice of parameters, the parent theory reproduces (i) the standard and exotic duals for p-forms and (ii) the standard and double duals for (p,1) bipartite tensor fields, such as the linearized graviton and the Curtright field. Moreover, we discuss how deformations related to codimension-1 branes are included in the parent theory.