Current algebras from QP-manifolds in general dimensions

Abstract

We propose a new unified formulation of the current algebra theory in general dimensions in terms of supergeometry. We take a QP-manifold, i.e. a differential graded (dg) symplectic manifold, as a fundamental framework. A Poisson bracket in a current algebra is constructed by the so called derived bracket of the graded Poisson structure induced from the above QP-structure. By taking a canonical transformation on a QP-manifold, correct anomalous terms in physical theories are derived. A large class of current algebras with and without anomalous terms (central extensions) are constructed from the above structure. Moreover, using this formulation, a new class of current algebras related higher structures are systematically obtained.

41 pages

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• Derived brackets
• WZW-Poisson manifolds
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Cited by in corpus (4)

• Lectures on AKSZ Sigma Models for Physicists
• Canonical Functions and Differential Graded Symplectic Pairs in Supergeometry and AKSZ Sigma Models with Boundary
• Brane current algebras and generalised geometry from QP manifolds
• Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds