S-duality action on discrete T-duality invariants

Abstract

In heterotic string theory compactified on T⁶, the T-duality orbits of dyons of charge (Q, P) are characterized by O(6, 22; R ) invariants Q², P² and Q·P together with a set of invariants of the discrete T-duality group O(6, 22; Z ). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that for dyons with torsion r, the degeneracy formula, expressed as a function of Q², P² and Q·P, is required to be manifestly invariant under only a subgroup of the S-duality group. This subgroup is isomorphic to Γ⁰(r). Our analysis also shows that for a given torsion r, all other discrete T-duality invariants are characterized by the elements of the coset SL(2, Z)/Γ⁰(r).