Twisted Sisters: KK Monopoles and their Zero Modes

TL;DR

This paper investigates the conditions under which fermionic zero modes exist in KK monopole backgrounds, revealing how real mass influences zero mode presence and impacting non-perturbative dynamics in supersymmetric theories.

Contribution

It provides a detailed analysis of fermionic zero modes in KK monopoles, highlighting the role of real mass and its implications for non-perturbative effects.

Findings

Zero modes exist only with sufficiently large real mass.

Large real mass causes decoupling of KK monopole effects.

Correct zero mode counting is crucial for understanding low-energy dynamics.

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 non-perturbative effects determining the low-energy dynamics.