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28 March 2024
 
  » arxiv » 1502.3510

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A mathematical foundation of Rozansky-Witten theory
Kwokwai Chan ; Naichung Conan Leung ; Qin Li ;
Date 12 Feb 2015
AbstractWe give a mathematically rigorous construction of Rozansky-Witten’s 3-dimensional $sigma$-model as a perturbative quantum field theory (QFT) by applying Costello’s approach using the Batalin-Vilkovisky (BV) formalism. The quantization of our model is obtained via the technique of configuration spaces. We also investigate the observable theory following the work of 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 hyperk"ahler manifold. We further give a mathematical definition of the partition function and prove that it coincides with the Rozansky-Witten invariants.
Source arXiv, 1502.3510
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