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Semidensities on Odd Symplectic Supermanifolds

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Abstract

We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new Δ-operator action on semidensities as the proper framework for the Batalin-Vilkovisky (BV) formalism. We establish relations between semidensities on E and differential forms on Lagrangian surfaces. We apply these results to Batalin-Vilkovisky geometry. Another application is to (1.1)-codimensional surfaces in E. We construct a kind of ‘‘pull-back’’ of semidensities to such surfaces. This operation and the Δ-operator are used for obtaining integral invariants for (1.1)-codimensional surfaces.

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  1. Department of Mathematics, University of Science and Technology (UMIST), Manchester, M60 1QD, UK

    Hovhannes M. Khudaverdian

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  1. Hovhannes M. Khudaverdian
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Correspondence to Hovhannes M. Khudaverdian.

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N. Nekrasov

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Khudaverdian, H. Semidensities on Odd Symplectic Supermanifolds. Commun. Math. Phys. 247, 353–390 (2004). https://doi.org/10.1007/s00220-004-1083-x

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