Hecke-Langlands Duality and Witten’s Gravitational Moonshine

The purpose of this research is to give a dual description conformal blocks d=2 rational CFT (conformal field theory) in terms Hecke eigenforms and eigensheaves. In particular, partition functions, characters lattice theta functions may be reconstructed from the action operators. This method can applied to: 1) rings integers Galois number fields equipped with trace (or anti-trace) form; 2) root lattices affine Kac-Moody algebras WZW-models; 3) minimal models Belavin-Polyakov-Zamolodchikov related spin-chain/lattice models; 4) vertex Leech Niemeier others. We also use original Witten’s idea construct 3-dimensional quantum gravity as AdS/CFT-dual c=24 Monster algebra Frenkel-Lepowsky- Meurman. Concerning geometric Langlands duality, we results Beilinson-Drinfeld, Frenkel-Ben-Zvi, Gukov-Kapustin-Witten many others (cf. references). main new result paper construction number-theoretical superalgebras Section 5 applications theories gravity.