Non-abelian Gerbes and Enhanced Leibniz Algebras

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 semistrict 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. Non-abelian Gerbes and Enhanced Leibniz Algebras. Phys.Rev.D, 2016, 94 (2), pp.021702. ⟨10.1103/PhysRevD.94.021702⟩. ⟨hal-01553971⟩

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