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A mathematical foundation of Rozansky-Witten theory | Kwokwai Chan
; Naichung Conan Leung
; Qin Li
; | Date: |
12 Feb 2015 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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