Monopoles for Gravitation and for Higher Spin Fields

TL;DR

This paper explores massless higher spin gauge theories with electric and magnetic sources, deriving equations of motion, a generalized quantization condition, and analyzing the gravitational Taub-NUT solution with both types of sources.

Contribution

It introduces a generalized Dirac quantization condition for higher spin fields and extends the analysis to nonlinear gravitation including Taub-NUT solutions.

Findings

Derived a generalized quantization condition involving asymptotic charges.

Established the variational principle for higher spin theories with sources.

Connected the quantization condition to angular momentum in gravity.

Abstract

We consider massless higher spin gauge theories with both electric and magnetic sources, with a special emphasis on the spin two case. We write the equations of motion at the linear level (with conserved external sources) and introduce Dirac strings so as to derive the equations from a variational principle. We then derive a quantization condition that generalizes the familiar Dirac quantization condition, and which involves the conserved charges associated with the asymptotic symmetries for higher spins. Next we discuss briefly how the result extends to the non linear theory. This is done in the context of gravitation, where the Taub-NUT solution provides the exact solution of the field equations with both types of sources. We rederive, in analogy with electromagnetism, the quantization condition from the quantization of the angular momentum. We also observe that the Taub-NUT metric is asymptotically flat at spatial infinity in the sense of Regge and Teitelboim (including their parity conditions). It follows, in particular, that one can consistently consider in the variational principle configurations with different electric and magnetic masses.