Current Algebras and QP Manifolds

Details Current Algebras and QP Manifolds Current Algebras and QP Manifolds

2011-08-02

arxiv.org/abs/1108.0473v2

Physics

High Energy Physics

High Energy Physics - Theory

24 pages

Scientific paper

Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets. We generalize their current algebras to higher dimensions. QP manifolds provide the unified structures of current algebras in any dimension. Current algebras give rise to structures of Leibniz/Loday algebroids, which are characterized by QP structures. Especially, in three dimensions, a current algebra has a structure of a Lie algebroid up to homotopy introduced by Uchino and one of the authors which has a bracket of a generalization of the Courant-Dorfman bracket. Anomaly cancellation conditions are reinterpreted as generalizations of the Dirac structure.

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