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Gauged extended field theory and generalized Cartan geometry

Falk Hassler*, David Osten†, and Alex Swash‡

  • *Contact author: falk.hassler@uwr.edu.pl
  • †Contact author: david.osten@uwr.edu.pl
  • ‡Contact author: alex.swash@uwr.edu.pl
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Phys. Rev. D 113, 066017 – Published 26 March, 2026

DOI: https://doi.org/10.1103/pzq2-1rhv

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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Phys. Rev. D 113, 066017– Published 26 March, 2026
  • Received 9 December 2025
  • Accepted 11 February 2026
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