Constraints on spacetime manifold in Euclidean supergravity in terms of Dirac eigenvalues

TL;DR

This paper extends the use of Dirac eigenvalues as observables in Euclidean supergravity by deriving the most general constraints on spacetime curvatures that allow these eigenvalues to serve as meaningful physical quantities.

Contribution

It provides a comprehensive set of constraints on spacetime and spinor bundle curvatures ensuring Dirac eigenvalues are valid observables in Euclidean supergravity.

Findings

Derived the most general constraints on spacetime curvatures

Established conditions for Dirac eigenvalues to be observables

Extended previous work on Dirac eigenvalues in supergravity

Abstract

We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold under which spacetime admits Dirac eigenvalues as observables, are derived.