Communications in Mathematical Physics

, Volume 355, Issue 1, pp 97–144

BV Quantization of the Rozansky–Witten Model

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Abstract

We investigate the perturbative aspects of Rozansky–Witten’s 3d \({\sigma}\)-model (Rozansky and Witten in Sel Math 3(3):401–458, 1997) using Costello’s approach to the Batalin–Vilkovisky (BV) formalism (Costello in Renormalization and effective field theory, American Mathematical Society, Providence, 2011). 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 (First European congress of mathematics, Paris, 1992) and Axelrod–Singer (J Differ Geom 39(1):173–213, 1994). We also study the factorization algebra structure of quantum observables following Costello–Gwilliam (Factorization algebras in quantum field theory, Cambridge University Press, Cambridge 2017). 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 we prove that the partition function reproduces the Rozansky–Witten invariants.

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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe Chinese University of Hong KongShatinHong Kong
  2. 2.The Institute of Mathematical Sciences and Department of MathematicsThe Chinese University of Hong KongShatinHong Kong
  3. 3.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina

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