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Finite-Dimensional AKSZ–BV Theories

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Abstract

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.

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Authors and Affiliations

  1. I.N.F.N. and Dipartimento di Fisica, Via G. Sansone 1, 50019, Sesto Fiorentino, Florence, Italy

    Francesco Bonechi

  2. Petersburg Department of V. A. Steklov Institute of Mathematics, Fontanka 27, 191023, St. Petersburg, Russia

    Pavel Mnëv

  3. Department of Physics and Astronomy, Uppsala University, Box 516, 751 20, Uppsala, Sweden

    Maxim Zabzine

Authors
  1. Francesco Bonechi
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  2. Pavel Mnëv
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  3. Maxim Zabzine
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Correspondence to Pavel Mnëv.

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Bonechi, F., Mnëv, P. & Zabzine, M. Finite-Dimensional AKSZ–BV Theories. Lett Math Phys 94, 197–228 (2010). https://doi.org/10.1007/s11005-010-0423-3

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  • DOI: https://doi.org/10.1007/s11005-010-0423-3

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