TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.5.5.051
TI  - The geometry of Casimir W-algebras
PY  - 2018/11/23
UR  - https://www.scipost.org/SciPostPhys.5.5.051
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 5
IS  - 5
SP  - 051
A1  - Belliard, Raphaël
AU  - Eynard, Bertrand
AU  - Ribault, Sylvain
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.5.5.051,
	title={{The geometry of Casimir W-algebras}},
	author={Raphaël Belliard and Bertrand Eynard and Sylvain Ribault},
	journal={SciPost Phys.},
	volume={5},
	pages={051},
	year={2018},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.5.5.051},
	url={https://scipost.org/10.21468/SciPostPhys.5.5.051},
}