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We introduce and study the Wilson loops in a general 3D topological fieldtheories (TFTs), and show that the expectation value of Wilson loops also givesknot invariants as in Chern-Simons theory. We study the TFTs within theBatalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ)framework, and the Ward identities of these theories imply that the expectationvalue of the Wilson loop is a pairing of two dual constructions of (co)cyclesof certain extended graph complex (extended from Kontsevich's graph complex toaccommodate the Wilson loop). We also prove that there is an isomorphismbetween the same complex and certain extended Chevalley-Eilenberg complex ofHamiltonian vector fields. This isomorphism allows us to generalize the Liealgebra weight system for knots to weight systems associated with anyhomological vector field and its representations. As an example we constructknot invariants using holomorphic vector bundle over hyperKahler manifolds.

Knot Invariants and New Weight Systems from General 3D TFTs