Electric Dipole Moment of a BPS Monopole

TL;DR

This paper constructs supersymmetric monopole superpartners in N=2 theories, revealing their operator-valued electric dipole moments proportional to fermionic zero-mode angular momentum, with implications for monopole dynamics.

Contribution

It introduces a method to construct monopole superpartners with operator-valued electric dipole moments linked to fermionic zero-modes.

Findings

Electric dipole moment operator proportional to fermionic zero-mode angular momentum

Gyroelectric ratio g=2 for the dipole moment

Magnetic quadrupole operator vanishes on all states

Abstract

Monopole ``superpartner'' solutions are constructed by acting with finite, broken supersymmetry transformations on a bosonic N=2 BPS monopole. The terms beyond first order in this construction represent the backreaction of the the fermionic zero-mode state on the other fields. Because of the quantum nature of the fermionic zero-modes, the superpartner solution is necessarily operator valued. We extract the electric dipole moment operator and show that it is proportional to the fermion zero-mode angular momentum operator with a gyroelectric ratio g=2. The magnetic quadrupole operator is shown to vanish identically on all states. We comment on the usefulness of the monopole superpartner solution for a study of the long-range spin dependent dynamics of BPS monopoles.