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arXiv · 1502.03510

BV quantization of the Rozansky-Witten model

Kwokwai Chan·Naichung Conan Leung·Qin Li
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Abstract

We investigate the perturbative aspects of Rozansky-Witten's 3d $σ$-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 $H^*(X,(\wedge^*T_X)^{\otimes g})$ (where $X$ is the target manifold), and prove that the partition function reproduces the Rozansky-Witten invariants.

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Kwokwai Chan, Naichung Conan Leung, Qin Li. 2017-05-02. BV quantization of the Rozansky-Witten model. https://doi.org/10.1007/s00220-017-2924-8

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