Conformal Virasoro Research Articles

R ( p , q ) -deformed conformal Virasoro algebra

This paper addresses an R(p,q)-deformed conformal Virasoro algebra with an arbitrary conformal dimension Δ. Well-known deformations constructed in the literature are deduced as particular cases. Then, the special case of the conformal dimension Δ = 1 is elucidated for its interesting properties. The R(p,q)− KdV equation, associated with the deformed Virasoro algebra, is also derived and discussed. Finally, the (p, q)-deformed energy-momentum tensor, consistent with the central extension term, is computed and analyzed.

Non-local matrix generalizations ofW-algebras

There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinarym th-order linear differential opeatorsL=−d m+U 1 d m−1+U 2 d m−2+...+U m . In this paper, I consider in detail the case where theU k aren×n-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifoldU 1=0. This reduction gives rise to matrix generalizations of (the classical version of) thenon-linear W m -algebras, calledV n, m -algebras. The non-commutativity of the matrices leads tonon-local terms in theseV n, m -algebra.s I show that these algebras contain a conformal Virasoro subalgebra and that combinationsW k of theU k can be formed that aren×n-matrices of conformally primary fields of spink, in analogy with the scalar casen=1. In general however, theV m, n -algebras have a much richer structure than theW m -algebras as can be seen on the examples of thenon-linear andnon-local Poisson brackets {(U 2)ab(σ), (U 2)cd(σ′)}, {(U 2)ab(σ), (W 3)cd(σ′)} and {(W 3)ab(σ), (W 3)cd(σ′)} which I work out explicitly for allm andn. A matrix Miura transformations is derived, mapping these complicated (second Gelfand-Dikii) brackets of theU k to a set of much simpler Poisson brackets, providing the analogoue of the free-field representation of theW m -algebras.