New infinite-dimensional symmetry groups for heterotic string theory

Abstract

Some Riemann-Hilbert (RH) problems are introduced for carrying out symmetry transformations of the 2-dimensional heterotic string theory. A pair of RH transformations are constructed, and they are verified to give an infinite-dimensional symmetry group of the considered theory. This symmetry group has the structure of the semidirect product of the Kac-Moody group $\stackrel{^}{O(d,d+n)}$ and Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated out, and they are found to give exactly the same results as in my previous paper. These demonstrate that the pair of RH transformations in the current paper provide exponentiations of all the infinitesimal symmetries in my previous paper. The finite forms of symmetry transformations given in the present paper are more important and useful for theoretic studies and new solution generation, etc.