Gauged extended field theory and generalized Cartan geometry

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Abstract
Cartan geometry provides a unifying algebraic construction of curvature and torsion, based on an underlying model Lie algebra; a viewpoint that can be extended naturally to the higher algebraic structures underlying supergravity. We present a Cartan-geometric framework for generalized geometries governed by a differential graded Lie algebra, extending previous results. The extended tangent bundle admits the action of both a global duality group G and a local gauge group H . This algebraic structure is implemented via a brane current algebra; the phase space Poisson structure of p -branes. Within this Cartan-inspired framework, we define a hierarchy of generalized connections and compute their linearized torsion and curvature tensors, including the higher curvatures required by the tensor hierarchy. This provides a systematic construction of curvature and torsion tensors in generic generalized geometries.
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Funding Information
  • Narodowe Centrum Nauki (2021/42/E/ST2/00304)
  • Narodowe Centrum Nauki (2024/55/D/ST2/01205)
  • Narodowe Centrum Nauki (2022/45/P/ST2/03995)
  • Horizon 2020 Framework Programme
  • H2020 Marie Skłodowska-Curie Actions (945339)

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