String branchings and complex tori and algebraic representations of generalized Krichever-Novikov algebras

TL;DR

This paper explores the structure and deformations of Krichever-Novikov algebras associated with complex tori and string propagation, revealing connections to the Virasoro algebra through central extensions.

Contribution

It introduces new algebraic structures and deformation behaviors of Krichever-Novikov algebras on complex tori with applications to string theory.

Findings

Calculated structure constants for Krichever-Novikov algebras.

Derived a central extension via b-c systems.

Showed deformation of the cocycle to the Virasoro cocycle.

Abstract

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point 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. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40