New infinite-dimensional hidden symmetries for heterotic string theory

Abstract

The symmetry structures of two-dimensional heterotic string theory are studied further. A $(2d+n)\ifmmode\times\else\texttimes\fi{}(2d+n)$ matrix complex $H$-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody $o(\stackrel{^}{d,d+n})$ and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected.