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arXiv · 2509.04595

Gauged Extended Field Theory and Generalised Cartan Geometry

Falk Hassler·David Osten·Alex Swash
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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 generalised geometries governed by a differential graded Lie algebra, extending previous results. The extended tangent bundle admits the action of both a global duality group $\mathcal{G}$ 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 generalised connections and compute their linearised 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 generalised geometries.

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Falk Hassler, David Osten, Alex Swash. 2025-09-04. Gauged Extended Field Theory and Generalised Cartan Geometry. https://arxiv.org/abs/2509.04595

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