Observables of the Euclidean Supergravity

TL;DR

This paper derives the constraints necessary for the eigenvalues of the Dirac operator to serve as dynamical variables in Euclidean supergravity, focusing on gauge invariance and eigenspinor restrictions.

Contribution

It introduces a new set of constraints linking Dirac eigenvalues to Euclidean supergravity, emphasizing gauge invariance and eigenspinor conditions.

Findings

Constraints for Dirac eigenvalues as dynamical variables are established.

Gauge invariance imposes specific conditions on eigenspinors.

Restrictions on eigenspinors are derived from the constraints.

Abstract

The set of constraints under which the eigenvalues of the Dirac operator can play the role of the dynamical variables for Euclidean supergravity is derived. These constraints arise when the gauge invariance of the eigenvalues of the Dirac operator is imposed. They impose conditions which restrict the eigenspinors of the Dirac operator.