Strong-Weak Coupling Duality in Three Dimensional String Theory

TL;DR

This paper demonstrates that in three-dimensional heterotic string theory, target space duality and strong-weak coupling duality unify into a larger symmetry group, revealing new insights into the spectrum and soliton solutions.

Contribution

It shows the unification of duality groups into O(8,24;Z) and explores its implications for the spectrum and soliton solutions in string theory.

Findings

Unification of duality groups into O(8,24;Z)

Prediction of harmonic forms on monopole moduli space

Relation of different soliton solutions via duality transformations

Abstract

Following an old result of Marcus and Schwarz we argue that in the heterotic string theory compactified on a seven dimensional torus, the target space duality group O(7,23;Z) and the strong-weak coupling duality transformations combine into the group O(8,24;Z). We discuss symmetry of the combined spectrum of elementary particles and solitons in the theory, and also show that the existence of this symmetry predicts the number of harmonic forms on the moduli space of periodic arrays of BPS monopoles in (3+1) dimensions. Finally, we show that the O(8,24;Z) transformations relate the soliton solutions of Dabholkar et. al. representing the fundamental string to the soliton solutions of Greene et. al. representing `stringy cosmic strings'.