Finite-Dimensional AKSZ¨CBV Theories

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• 作者：Francesco Bonechi ; Pavel Mn?v and Maxim Zabzine
• 关键词：topological quantum field theory ; Batalin– ; Vilkovisky quantization ; Poisson geometry ; Courant geometry
• 刊名：Letters in Mathematical Physics
• 出版年：2010
• 出版时间：November 2010
• 年：2010
• 卷：94
• 期：2
• 页码：197-228
• 全文大小：361.4 KB

文摘

We describe a canonical reduction of AKSZ–BV theories to the cohomology of the source manifold. We get a finite-dimensional BV theory that describes the contribution of the zero modes to the full QFT. Integration can be defined and correlators can be computed. As an illustration of the general construction, we consider two-dimensional Poisson sigma model and three-dimensional Courant sigma model. When the source manifold is compact, the reduced theory is a generalization of the AKSZ construction where we take as source the cohomology ring. We present the possible generalizations of the AKSZ theory.