• DOI:10.1006/aphy.2002.6283
• Corpus ID: 15714024

Gerbes and duality

@article{Caicedo2002GerbesAD,
  title={Gerbes and duality},
  author={Mario I. Caicedo and Ignacio Mart{\'i}n and Alvaro Restuccia},
  journal={Annals of Physics},
  year={2002},
  volume={300},
  pages={32-53}
}

• M. Caicedo, I. Martín, A. Restuccia
• Published 30 April 2002
• Mathematics
• Annals of Physics

Abstract 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 the d=11 supermembrane and d=10 IIA Dirichlet supermembrane.