We show that the continuous limit of a wide natural class of the right-invariant discrete Lagrangian systems on the Virasoro group gives the family of integrable PDE's containing Camassa-Holm, Hunter-Saxton and Korteweg-de Vries equations. This family has been recently derived by Khesin and Misio lek as Euler equations on the Virasoro algebra for H 1 α,β-metrics. Our result demonstrates a unive...

We use the Regge-Teitelboim method to treat surface integrals in gauge theories to find global charges in Chern-Simons theory. We derive the affine and Virasoro generators as global charges associated with symmetries of the boundary. The role of boundary conditions is clarified. We prove that for diffeomorphisms that do not preserve the boundary there is a classical contribution to the central ...

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with m arbitrary time-dependent coefficients are obtained possessing symmetries involving m arbitrary functions of time. A particular grade...

We analyze the near horizon symmetry of extremal Kerr black hole within framework Poincar\'e gauge theory (PG) for two important limiting cases: Riemannian and teleparallel solution. show that algebra canonical generators is realized by Virasoro algebra, with central charge which depends on radius . The conformal entropy obtained via Cardy formula.

The metric determines the casual structure of spacetime, but in quantum gravity it is also a dynamical field which must be quantized using this causal structure; this is the famous problem of time. A radical resolution of this paradox is proposed: remove the concept of space-like separation entirely. This can be done by describing all fields in terms on p-jets, living on the observer’s trajecto...

Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo–conformal representation. In special cases, this representation reduces to ordinary– or logarithmic–conformal field theory. There are, however, other cases in which the Green functions differ from those of ordinary– or logarithmic–conformal field theories. This representat...