Higher-degree Dirac Currents of Twistor and Killing Spinors in Supergravity Theories

TL;DR

This paper explores how higher degree Dirac currents derived from twistor and Killing spinors reveal hidden spacetime symmetries in supergravity theories, extending known concepts to higher forms and dimensions.

Contribution

It introduces the correspondence between higher degree Dirac currents and hidden symmetries, generalizes Dirac currents to higher degrees, and relates these to supergravity equations in 10 and 11 dimensions.

Findings

Higher degree Dirac currents correspond to hidden spacetime symmetries.

These currents satisfy Maxwell-like and Duffin-Kemmer-Petiau equations.

The correspondence holds across different inner product classes in supergravity.

Abstract

We show that higher degree Dirac currents of twistor and Killing spinors correspond to the hidden symmetries of the background spacetime which are generalizations of conformal Killing and Killing vector fields respectively. They are the generalizations of 1-form Dirac currents to higher degrees which are used in constructing the bosonic supercharges in supergravity theories. In the case of Killing spinors, we find that the equations satisfied by the higher degree Dirac currents are related to Maxwell-like and Duffin-Kemmer-Petiau equations. Correspondence between the Dirac currents and harmonic forms for parallel and pure spinor cases is determined. We also analyze the supergravity twistor and Killing spinor cases in 10 and 11-dimensional supergravity theories and find that although different inner product classes induce different involutions on spinors, the higher degree Dirac currents still correspond to the hidden symmetries of the spacetime.