Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-09-15
Nucl.Phys. B558 (1999) 391-415
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, LaTex. The proposal is restricted to first order theories. An appendix is added. Some references are added
Scientific paper
10.1016/S0550-3213(99)00392-2
We propose a new "Hamiltonian inspired" covariant formula to define (without harmful ambiguities) the superpotential and the physical charges associated to a gauge symmetry. The criterion requires the variation of the Noether current not to contain any derivative terms in $\partial_{\mu}\delta \f$. The examples of Yang-Mills (in its first order formulation) 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 for a particular choice of boundary conditions. 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 is also computed. However, no associated central charge is found for $n \geq 2$. Finally, we treat the abelian p-form Chern-Simons theory in a similar way.
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