3 research outputs found
The geometry of Casimir W-algebras
Let be a simply laced Lie algebra,
the corresponding affine Lie algebra at level one, and
the corresponding Casimir W-algebra. We consider
-symmetric conformal field theory on the Riemann
sphere. To a number of -primary fields, we associate
a Fuchsian differential system. We compute correlation functions of
-currents in terms of solutions of that system, and
construct the bundle where these objects live. We argue that cycles on that
bundle correspond to parameters of the conformal blocks of the W-algebra,
equivalently to moduli of the Fuchsian system
The geometry of Casimir W-algebras
13 pagesInternational audienceLet be a simply laced Lie algebra, the corresponding affine Lie algebra at level one, and the corresponding Casimir W-algebra. We consider -symmetric conformal field theory on the Riemann sphere. To a number of -primary fields, we associate a Fuchsian differential system. We compute correlation functions of -currents in terms of solutions of that system, and construct the bundle where these objects live. We argue that cycles on that bundle correspond to parameters of the conformal blocks of the W-algebra, equivalently to moduli of the Fuchsian system