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arXiv · 1308.0100

Current algebras from QP-manifolds in general dimensions

Noriaki Ikeda·Xiaomeng Xu
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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.

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Noriaki Ikeda, Xiaomeng Xu. 2013-08-01. Current algebras from QP-manifolds in general dimensions. https://arxiv.org/abs/1308.0100

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