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A Kähler structure of the triplectic geometry

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Abstract

We study the geometry of the triplectic quantization of gauge theories. We show that the triplectic geometry is determined by the geometry of a Kähler manifoldN endowed with a pair of transversal polarizations. The antibrackets can be brought to the canonical form if and only ifN admits a flat symmetric connection that is compatible with the complex structure and the polarizations.

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Authors and Affiliations

  1. Tamm Department of Theoretical Physics, Lebedev Physical Institute, RAS, Moscow, Russia

    M. A. Grigoriev & A. M. Semikhatov

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  1. M. A. Grigoriev
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  2. A. M. Semikhatov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 355–372, September, 2000.

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Grigoriev, M.A., Semikhatov, A.M. A Kähler structure of the triplectic geometry. Theor Math Phys 124, 1157–1171 (2000). https://doi.org/10.1007/BF02550995

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