Magnetic Monopoles, Bogomol'nyi Bound and SL(2,Z) Invariance in String Theory

TL;DR

This paper demonstrates that in heterotic string theory compactified on a six-dimensional torus, the Bogomol'nyi bound on dyon mass remains invariant under SL(2,Z) duality, linking monopoles and elementary particles through strong-weak coupling symmetry.

Contribution

It establishes SL(2,Z) invariance of the Bogomol'nyi bound and identifies monopole solutions related to elementary particles via duality in heterotic string theory.

Findings

The Bogomol'nyi bound is invariant under SL(2,Z) transformations.

Elementary string excitations satisfy the Bogomol'nyi bound.

Monopoles are related to elementary particles with matching mass and degeneracy.

Abstract

We show that in heterotic string theory compactified on a six dimensional torus, the lower bound (Bogomol'nyi bound) on the dyon mass is invariant under the SL(2,Z) transformation that interchanges strong and weak coupling limits of the theory. Elementary string excitations are also shown to satisfy this lower bound. Finally, we identify specific monopole solutions that are related via the strong-weak coupling duality transformation to some of the elementary particles saturating the Bogomol'nyi bound, and these monopoles are shown to have the same mass and degeneracy of states as the corresponding elementary particles.