Multiplicative vector fields on bundle gerbes

Derek Krepski; Jennifer Vaughan

doi:10.1016/j.difgeo.2022.101931

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arXiv · 2003.12874

Multiplicative vector fields on bundle gerbes

Derek Krepski·Jennifer Vaughan

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Abstract

Infinitesimal symmetries of $S^1$-bundle gerbes are modelled with multiplicative vector fields on Lie groupoids. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector fields to the bundle gerbe, and that the 3-curvature presents the obstruction to the horizontal lift being a morphism of Lie 2-algebras. Connection-preserving multiplicative vector fields on a bundle gerbe with connective structure are shown to inherit a natural Lie 2-algebra structure; moreover, this Lie 2-algebra is canonically quasi-isomorphic to the Poisson-Lie 2-algebra of the 2-plectic base manifold $(M,χ)$, where $χ$ is the 3-curvature of the connective structure. As an application of this result, we give analogues of a formula of Kostant in the 2-plectic and quasi-Hamiltonian context.

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BibTeX RIS

Derek Krepski, Jennifer Vaughan. 2021-11-04. Multiplicative vector fields on bundle gerbes. https://doi.org/10.1016/j.difgeo.2022.101931

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