Beyond affine Kac-Moody algebras in string theory

Abstract

This work is devoted to the study of certain infinite-dimensional Lie algebras arising in string theory. The two investigated models describe a chiral sector of a fully compactified closed bosonic string moving on a subcritical 10-dimensional or a critical 26-dimensional spacetime torus, respectively. To analyze the corresponding Lie algebra of physical states, a discrete version of the DDF construction in the framework of vertex algebras is developed. When applied to the subcritical example, the method yields some new insights into the complicated structure of the hyperbolic Kac-Moody algebra E_1_0 in terms of transversal and longitudinal states. Due to the no-ghost theorem, in 26 dimensions only transversal physical states appear which make up the so-called fake monster Lie algebra. The latter represents an example of a Borcherds algebra, which is a generalized Kac-Moody algebras in the sense that imaginary simple roots are allowed for in the defining relations. It is demonstrated for the example, that this feature can be understood by means of the DDF operators, too. Finally, a new result representation theory of these algebras is proved which is analyzed in view of possible applications to physics. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(94-209) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman