Vertex operator for generalized Kac-Moody algebras associated to the two-sphere and the two-torus
Abstract
We pursue our study of generalized Kac-Moody and Virasoro algebras defined on compact homogeneous manifolds. Extending the well-known vertex operator in the case of the two-torus or the two-sphere, we obtain explicit bosonic realizations of the semi-direct product of the extension of Kac-Moody and Virasoro algebras on π1 Γ π1 and π2, respectively. As for the fermionic realization previously constructed, in order to have well defined algebras, we introduce, beyond the usual normal ordering prescription, a regulator and regularize infinite sums by means of the Riemann ΞΆ-function.
- Publication:
-
Modern Physics Letters A
- Pub Date:
- December 2022
- DOI:
- 10.1142/S021773232250239X
- arXiv:
- arXiv:2211.04201
- Bibcode:
- 2022MPLA...3750239C
- Keywords:
-
- KacβMoody;
- Virasoro algebras;
- bosons realization;
- regularization;
- 02.20.Tw;
- 03.65.Fd;
- 11.25.Hf;
- Infinite-dimensional Lie groups;
- Algebraic methods;
- Conformal field theory algebraic structures;
- Mathematical Physics;
- High Energy Physics - Theory;
- Mathematics - Representation Theory
- E-Print:
- Detailed description of the Hilbert space, references added, to appear in Mod. Phys. Lett. A