Abstract
We find the conditions for the existence of fermionic zero modes of the fundamental representation in the background of a Kaluza-Klein (KK) monopole. We show that while there is no zero mode without a real mass, a normalizable zero mode appears once the real mass is sufficiently large. This provides an elegant explanation for the known decoupling of KK monopole effects in supersymmetric theories when a large real mass term is added. We also present an application where the correct counting of KK zero modes plays an essential role in understanding the nonperturbative effects determining the low-energy dynamics.
Highlights
Introduction.—Magnetic monopoles can have important dynamical and phenomenological consequences under a wide variety of circumstances. They can appear as massive extended objects in grand unified theories (GUTs), their existence can explain charge quantization, or they can be responsible for nonperturbative effects in strongly coupled gauge theories
Many of the nonperturbative effects in the 4D SUSY gauge theories can be best understood by considering the theory on the circle, and eventually taking the infinitely large radius limit
Our results provide an intuitive explanation of KK monopole decoupling in the limit of a large real mass: for a sufficiently large real mass the KK monopole acquires additional fundamental fermion zero modes, and as a result the KK monopole cannot correspond to a superpotential term
Summary
Introduction.—Magnetic monopoles can have important dynamical and phenomenological consequences under a wide variety of circumstances. The essential property of monopoles that largely determines the structure of the induced superpotential terms is the number of fermionic zero modes in a given monopole background. The Callias index theorem [14,15] specifies the number of fermionic zero modes in different gauge group representations for a given monopole background.
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