Current algebra and generalized Cartan geometry

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Abstract
This article shows that the approach to generalized curvature and torsion pioneered by Poláček and Siegel [Natural curvature for manifest T-duality, .] is a generalization of Cartan geometry—rendering latter natural from the point of view of O ( d , d ) -generalized geometry. We present this approach in the generalized metric formalism and show that almost all parts of the additional higher generalized tensors appearing in this approach correspond to covariant derivatives of the generalized Riemann tensor. As an application, we use this framework to phrase σ -model dynamics in an explicitly covariant way—both under generalized diffeomorphisms and local gauge transformations. Published by the American Physical Society 2024
Funding Information
  • Narodowe Centrum Nauki (2021/42/E/ST2/00304, 2022/45/P/ST2/03995)
  • Fonds Wetenschappelijk Onderzoek
  • Vlaamse regering (G006119N)
  • Vrije Universiteit Brussel
  • H2020 Marie Skłodowska-Curie Actions (945339)
  • SONATA BIS

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