On Superpotentials and Charge Algebras of Gauge Theories
Abstract
We propose a new "Hamiltonian inspired" covariant formula to define the superpotential of a gauge symmetry, and the physical charges associated to it. This follows from the similarities which exist between the canonical formalism and the cascade equation techniques. Following the Hamiltonian formalism, the idea is to require the variation of the Noether current to be "well defined" in a sense to be made precise. The examples of Yang-Mills and 3-dimensional Chern-Simons theories are revisited and the corresponding charge algebras (with their central extensions in the Chern-Simons case) are computed in a straightforward way. We then generalize the previous results to any (2n+1)-dimensional non-abelian Chern-Simons theory. We compute explicitly the superpotential associated to the non-abelian gauge symmetry which is nothing but the Chern-Simons Lagrangian in (2n-1) dimensions. The corresponding charge algebra generalizes in a natural way the Affine Kac-Moody Lie algebra of the 3-dimensional case. The associated central charge is also given. Finally, we treat the abelian p-form Chern-Simons theory in a similar way.Keywords
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