F & H Monopoles

TL;DR

This paper constructs and analyzes supersymmetric monopole solutions in heterotic string theory, revealing their dualities, geometries, and supersymmetry properties, including infinite towers of non-singular monopoles with complex structures.

Contribution

It introduces a broad class of heterotic string monopoles with T duality covariance, including non-singular solutions with bottomless throat geometries and enhanced world-sheet supersymmetry.

Findings

Massive F=H monopoles are T self-dual.

Massless F=-H monopoles are invariant under T duality and charge conjugation.

All monopoles can be exact supersymmetric solutions with enhanced world-sheet supersymmetry.

Abstract

Supersymmetric monopoles of the heterotic string theory associated with arbitrary non-negative number of the left moving modes of the string states are presented. They include H monopoles and their T dual partners F monopoles (ALE instantons). Massive F = H monopoles are T self-dual. Solutions include also an infinite tower of generic T duality covariant non-singular in stringy frame F\&H monopoles with the bottomless throat geometry. The massless F = -H monopoles are invariant under combined T duality and charge conjugation converting a monopole into anti monopole. All F\&H monopoles can be promoted to the exact supersymmetric solutions of the heterotic string theory since the holonomy group is the compact $SO(9)$. The sigma models for ${\bf M}^8$ monopoles, which admit constant complex structures, have enhanced world-sheet supersymmetry: (4,1) in general and (4,4) for the left-right symmetric monopoles. The space-time supersymmetric GS light-cone action in monopole background is directly convertible into the world-sheet supersymmetric NSR action.