2019/10/23 by Roberto Bonezzi, Olaf Hohm, Bonezzi, Roberto +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.1910.10399
40 pages
arxiv created 2019/10/23 · arxiv updated 2019/10/24
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by `infinity-enhanced Leibniz algebras' defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. We use this observation to streamline the construction of general tensor hierarchies, and we formulate dynamics in terms of a hierarchy of first-order duality relations, including scalar fields with a potential.