On Local Constraints of D=4 Supergravity in Terms of Dirac Eigenvalues

TL;DR

This paper explores the constraints necessary for Dirac eigenvalues to serve as observables in Euclidean supergravity, analyzing their relationships and linear dependencies within the covariant phase space.

Contribution

It provides a detailed analysis of the relationships among constraints in supergravity and derives conditions for their linear independence.

Findings

Constraints among Dirac eigenvalues are non-linear.

Derived equations for linear dependency of constraints.

Clarified conditions for constraints to be linearly independent.

Abstract

It has been recently shown that in order to have Dirac eigenvalues as observables of Euclidean supergravity, certain constraints should be imposed on the covariant phase space as well as on Dirac eigenspinors. We investigate the relationships among the constraints in the first set and argue that these relationships are not linear. We also derive a set of equations expressing the linear dependency of the constraints in order that the second set of constraints be linearly independent.