W-algebras from symplectomorphisms

Details W-algebras from symplectomorphisms W-algebras from symplectomorphisms

1999-12-21

arxiv.org/abs/hep-th/9912202v1

J.Math.Phys. 41 (2000) 2233-2250

Physics

High Energy Physics

High Energy Physics - Theory

LaTex, 25 pages, no figures, to appear in Journ. Math. Phys

Scientific paper

10.1063/1.533236

It is shown how $W$-algebras emerge from very peculiar canonical transformations with respect to the canonical symplectic structure on a compact Riemann surface. The action of smooth diffeomorphisms of the cotangent bundle on suitable generating functions is written in the BRS framework while a $W$-symmetry is exhibited. Subsequently, the complex structure of the symmetry spaces is studied and the related BRS properties are discussed. The specific example of the so-called $W_3$-algebra is treated in relation to some other different approaches.

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