2002/05/02 by M.I. Caicedo, M. I. Caicedo, I. Martin +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Antisymmetric relation #Black Holes and Theoretical Physics #Canonical quantization #Dirac (video compression format) #Duality (order theory) #Equivalence (formal languages) #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #Quantum field theory #T-duality #hep-th
paper · pdf · doi:10.1006/aphy.2002.6283
published as Annals Phys. 300 (2002) 32-53 · 47 pages, 1 figure, 2 references added
arxiv created 2002/05/02 · openalex publication_date 2002/08/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes, these objects are mathematical constructions generalizing U(1) bundles and are similarly classified by quantized charges. We address the duality maps in terms of the potentials rather than on their field strengths and show the quantum equivalence between dual theories which in turn allows a rigorous proof of a generalized Dirac quantization condition on the couplings. Our approach needs the introduction of an auxiliary form satisfying a global constraint which in the case of 1-form potentials coincides with the quantization of the magnetic flux. We apply our global approach to refine the proof of the duality equivalence between d=11 supermembrane and d=10 IIA Dirichlet supermembrane.