BV quantization of the Rozansky-Witten model

Abstract

We investigate the perturbative aspects of Rozansky-Witten's 3d $\sigma$-model using Costello's approach to the Batalin-Vilkovisky (BV) formalism. We show that the BV quantization (in Costello's sense) of the model, which produces a perturbative quantum field theory, can be obtained via the configuration space method of regularization due to Kontsevich and Axelrod-Singer. We also study the factorization algebra structure for quantum observables following Costello-Gwilliam. In particular, we show that the cohomology of local quantum observables on a genus $g$ handle body is given by $H^{\ast }(X,({\wedge }^{\ast }{T}_X{)}^{\otimes g})$ (where $X$ is the target manifold), and prove that the partition function reproduces the Rozansky-Witten invariants.

51 pages, 27 figures. v3: minor modifications, references added, final version to appear in CMP

References in corpus (3)

• Renormalisation and the Batalin-Vilkovisky formalism
• Gauge theory and mirror symmetry
• Rozansky-Witten invariants of hyperkähler manifolds

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• A one-loop exact quantization of Chern-Simons theory
• Lie algebroids as $L_{\infty }$ spaces
• Extended TQFTs and Algebraic Geometry
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
• Quantizing Derived Mapping Stacks