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arXiv · 1607.00060

Non-abelian Gerbes and Enhanced Leibniz Algebras

Thomas Strobl
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Abstract

We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge invariant functional enforces that the most general semi-strict Lie 2-algebra describing the bundle of a non-abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p, solved here for p = 2.

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Thomas Strobl. 2016-06-30. Non-abelian Gerbes and Enhanced Leibniz Algebras. https://doi.org/10.1103/physrevd.94.021702

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