Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes

Abstract

We investigate the generic 3D topological field theory within AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the perturbative partition function gives rise to secondary characteristic classes. We investigate a toy model which is an odd analogue of Chern-Simons theory, and we give some explicit computation of two point functions and show that its perturbation theory is identical to the Chern-Simons theory. We give concrete example of the homomorphism taking Lie algebra cocycles to Q-characteristic classes, and we reinterpreted the Rozansky-Witten model in this light.

52 pages

References in corpus (3)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Graph cohomology classes in the Batalin-Vilkovisky formalism
• On the AKSZ formulation of the Rozansky-Witten theory and beyond

Cited by in corpus (8)

• Harmonic Superspace Gaugeon Formalism for the ABJM Theory
• The BV Formalization of Chern-Simons Theory on Deformed Superspace
• Deformed Super-Yang-Mills in Batalin-Vilkovisky Formalism
• Knot Invariants and New Weight Systems from General 3D TFTs
• Equivariant Rozansky-Witten classes and TFTs
• BV quantization of the Rozansky-Witten model
• The second homology group of the commutative case of Kontsevich's symplectic derivation Lie algebra
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism