| Summary: | Let $\mathfrak{g}$ be a simply laced Lie algebra, $\widehat{\mathfrak{g}}_1$
the corresponding affine Lie algebra at level one, and
$\mathcal{W}(\mathfrak{g})$ the corresponding Casimir W-algebra. We consider
$\mathcal{W}(\mathfrak{g})$-symmetric conformal field theory on the Riemann
sphere. To a number of $\mathcal{W}(\mathfrak{g})$-primary fields, we associate
a Fuchsian differential system. We compute correlation functions of
$\widehat{\mathfrak{g}}_1$-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.
|
|---|
