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Unimodular homotopy algebras and Chern-Simons theory

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arxiv 1309.3219 v3 pith:LWQU25XM submitted 2013-09-12 math.QA hep-thmath.AGmath.AT

Christopher Braun , Andrey Lazarev This is my paper · ORCID
classification math.QAhep-thmath.AGmath.AT
keywords l-infinityalgebraalgebrashomotopyunimodularchern-simonsquantumanalyzed
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Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the structure of an L-infinity algebra whose homotopy type is a homotopy invariant of M. We formulate necessary and sufficient conditions for this L-infinity algebra to have a quantum lift. We also obtain structural results on unimodular L-infinity algebras and introduce a doubling construction which links unimodular and cyclic L-infinity algebras.

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  1. Full S-matrices and Witten diagrams with (relative) L-infinity algebras

    hep-th 2024-12 conditional novelty 7.0 of 10

    Cyclic relative L-infinity algebras encode the full S-matrix, including its trivial part, and reproduce Witten diagrams including CFT two-point functions.

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