Zero Modes of the Dirac Operator for regular Einstein-Yang-Mills Background fields

TL;DR

This paper proves the existence of normalizable zero modes of the twisted Dirac operator in a broad class of static Einstein-Yang-Mills backgrounds, including all regular, asymptotically flat, CP-symmetric configurations with specific properties.

Contribution

It establishes a general proof for zero modes in Einstein-Yang-Mills backgrounds for any gauge group and representation, covering a wide class of physically relevant solutions.

Findings

Zero modes exist for all regular, asymptotically flat, CP-symmetric Einstein-Yang-Mills backgrounds.

The proof applies to any gauge group and arbitrary spinor representation.

Includes all neutral, spherically symmetric configurations with purely magnetic gauge potentials.

Abstract

The existence of normalizable zero modes of the twisted Dirac operator is proven for a class of static Einstein-Yang-Mills background fields with a half-integer Chern-Simons number. The proof holds for any gauge group and applies to Dirac spinors in an arbitrary representation of the gauge group. The class of background fields contains all regular, asymptotically flat, CP-symmetric configurations with a connection that is globally described by a time-independent spatial one-form which vanishes sufficiently fast at infinity. A subset is provided by all neutral, spherically symmetric configurations which satisfy a certain genericity condition, and for which the gauge potential is purely magnetic with real magnetic amplitudes.