STRING BRANCHINGS ON COMPLEX TORI AND ALGEBRAIC REPRESENTATIONS OF GENERALIZED KRICHEVER-NOVIKOV ALGEBRAS

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two- and three-point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b - c systems. The defining cocycle for this central extension deforms to the well-known Virasoro cocycle for certain kinds of degenerations of the torus.