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arXiv · 1904.11036

Leibniz Gauge Theories and Infinity Structures

Roberto Bonezzi·Olaf Hohm
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Abstract

We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based on `tensor hierarchies', which describe towers of $p$-form gauge fields transforming under non-abelian gauge symmetries and which have been constructed up to low levels. Here we define `infinity-enhanced Leibniz algebras' that guarantee the existence of consistent tensor hierarchies to arbitrary level. We contrast these algebras with strongly homotopy Lie algebras ($L_{\infty}$ algebras), which can be used to define topological field theories for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries an associated $L_{\infty}$ algebra, which we discuss.

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Roberto Bonezzi, Olaf Hohm. 2019-04-24. Leibniz Gauge Theories and Infinity Structures. https://doi.org/10.1007/s00220-020-03785-2

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