S-duality Action on Discrete T-duality Invariants

TL;DR

This paper investigates how S-duality acts on discrete T-duality invariants of dyons in heterotic string theory, revealing that the degeneracy formula's invariance is restricted to a specific subgroup of the S-duality group, depending on torsion.

Contribution

It analyzes the interplay between S-duality and discrete T-duality invariants, identifying the subgroup mma^0(r) under which the dyon degeneracy formula remains invariant.

Findings

Degeneracy formula invariant under mma^0(r) subgroup for dyons with torsion r

Discrete T-duality invariants characterized by elements of SL(2,Z)/mma^0(r)

S-duality action constrains the invariance properties of dyon degeneracies

Abstract

In heterotic string theory compactified on T^6, the T-duality orbits of dyons of charge (Q,P) are characterized by O(6,22;R) invariants Q^2, P^2 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 Q^2, P^2 and Q.P, is required to be manifestly invariant under only a subgroup of the S-duality group. This subgroup is isomorphic to \Gamma^0(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)/\Gamma^0(r).