KN Algebra Derived from Virasoro Algebra with Vertex Operators

Abstract

Recently there have been several intensive attempts to study conformal field theories over a higher-genus Riemann surface r by means of operator formalisms. )-7) More recently Krichever and N ovikov have introduced a new kind of algebra (KN algebra) onto r as a natural extension of the Virasoro algebra.),9) This KN algebra contains also a subspace responsible for the Teichmliller deformations (see footnote on p. 166). In a series of papers)-14) Bonora et al. have applied the KN formalism to construct the BRST charge, Kac-Moody algebra, a global operator formalism for be systems and so on. Other contributions on this line can be found in Refs. 15)~20). In this paper we consider a system in which external fields such as tachyon field, symmetric and antisymmetric massless tensor fields are interacting with the closed bosonic string. By using the Virasoro algebra for such an interacting string we derive the corresponding KN algebra with vertex operators. We make use of the holomorphic property of integrand in the KN generator L i . This property allows us to relate the KN generator with the Virasoro generator. ) The Virasoro algebra with vertex operators is known to hold only when the mass of tachyon is a' m=-4 and external massless tensor fields satisfy the Lorentz condition.) Then such a derivation becomes possible. In § 2 we summarize the KN bases. In § 3 the KN algebra with vertex operators is derived from the Virasoro algebra with vertex operators. In § 4 we consider the same problem for the ghost b-e system. The final section is devoted to concluding remarks.