Higher-dimensional loop algebras, non-abelian extensions and p-branes

1994/01/31 by M. Cederwall, Martin Cederwall, Gabriele Ferretti +5 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Covariant transformation #Curvature #Filtered algebra #Generalization #Homotopy and Cohomology in Algebraic Topology #Loop (graph theory) #Operator algebra #hep-th

paper · pdf · doi:10.1016/0550-3213(94)90090-6

published as Nucl.Phys. B424 (1994) 97-123 · (published version, extended introduction), 35 pp.(LaTeX), Goteborg ITP-93-37

openalex publication_date 1994/08/01 · arxiv created 1994/09/08 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We postulate a new type of operator algebra with a non-abelian extension. This algebra generalizes the Kac--Moody algebra in string theory and the Mickelsson--Faddeev algebra in three dimensions to higher-dimensional extended objects (p-branes). We then construct new BRST operators, covariant derivatives and curvature tensors in the higher-dimensional generalization of loop space.

Citations

• Strong-weak coupling duality and non-perturbative effects in string theory
• Current Algebra in Three Dimensions
• Gauge theories and magnetic charge
• Topological charges for N = 4 supersymmetric gauge theories and monopoles of spin 1
• Magnetic monopoles as gauge particles?
• Hilbert space cocycles as representations of (3 + 1)-d current algebras
• Lie algebras associated with generalized Cartan matrices
• Heterotic solitons

Cited by

• On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations