Spectrum-generating functions for strings and superstrings

Abstract

The spectrum-generating functions for a variety of strings and superstrings are derived. These are expressed in terms of characters of irreducible representations of the appropriate transverse spacetime symmetry group and, in the case of heterotic strings, the relevant gauge group E8*E8 or Spin(32)/Z2. The expansions involve principal specialisations of characters of both GL(N) and GL(M/N) in the limit as M and N tend to infinity. By using Schur function methods, modification rules and various theta function identities a number of spectrum-generating functions are derived and tabulated. The equivalence of the GSO-projected Neveu-Schwarz-Ramond superstring and the Green-Schwarz superstring is proved, and the connection between the lattice formulation and the GSO-projected Neveu-Schwarz-Ramond formulation of heterotic strings is spelled out.