A systematic Cartan-geometric construction of linearised torsion and curvature hierarchies for generalised geometries with global duality group G and local gauge group H, realised via brane current algebras.
Tensor hierarchies and Leibniz algebras
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abstract
Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can canonically associate a tensor hierarchy to any Loday algebra. By formalizing the construction that is performed in supergravity, we build this tensor hierarchy explicitly. We show that this tensor hierarchy can be canonically equipped with a differential graded Lie algebra structure that coincides with the one that is found in supergravity theories.
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Gauged Extended Field Theory and Generalised Cartan Geometry
A systematic Cartan-geometric construction of linearised torsion and curvature hierarchies for generalised geometries with global duality group G and local gauge group H, realised via brane current algebras.