Twist-field representations of W-algebras, exact conformal blocks and character identities

@article{Bershtein2017TwistfieldRO,
  title={Twist-field representations of W-algebras, exact conformal blocks and character identities},
  author={Mikhail Bershtein and Pavlo Gavrylenko and Andrei Vladimirovich Marshakov},
  journal={Journal of High Energy Physics},
  year={2017},
  volume={2018},
  pages={1-56}
}
  • Mikhail Bershtein, Pavlo Gavrylenko, Andrei Vladimirovich Marshakov
  • Published 2017
  • Physics, Mathematics
  • Journal of High Energy Physics
  • A bstractWe study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of characters of these representations leads to nontrivial identities involving lattice theta-functions. We also propose a way to calculate their exact conformal blocks, expressing them for D-series in terms of geometric data of the corresponding Prym variety for covering curve with involution.