Symmetry algebras in Chern-Simons theories with boundary: canonical approach

I consider the classical Kac-Moody algebra and Virasoro algebra in Chern-Si mons theory with boundary within Dirac's canonical method and Noether's pro cedure. It is shown that the usual (bulk) Gauss law constraint becomes a se cond-class constraint because of the boundary effect. From this fact, the D irac bracket can be constructed explicitly without introducing additional g auge conditions and the classical Kac-Moody and Virasoro algebras are obtai ned within the usual Dirac method, The equivalence to the symplectic reduct ion method is presented and the connection to the Banados' work is clarifie d. Also the generalization to the Yang-Mills-Chem-Simons theory is consider ed where the diffeomorphism symmetry is broken by the (three-dimensional) Y ang-Mills term, In this case, the same Kac-Moody algebras are obtained alth ough the two theories are sharply different in the canonical structures. Bo th models realize the holography principle explicitly and the pure CS theor y reveals the correspondence of the Chern-Simons theory with boundary/confo rmal field theory, which is more fundamental and generalizes the conjecture d anti-de Sitter/conformal field theory correspondence. (C) 1999 Elsevier S cience B.V.