On the Dirac Eigenvalues as Observables of the on-shell N=2 D=4 Euclidean Supergravity

TL;DR

This paper extends the concept of Dirac eigenvalues as observables to on-shell N=2 D=4 Euclidean supergravity, defining their Poisson brackets within the covariant phase space.

Contribution

It generalizes previous work on Dirac eigenvalues to on-shell N=2 supergravity and computes their Poisson brackets in the covariant phase space.

Findings

Defined the covariant phase space for on-shell N=2 supergravity

Computed Poisson brackets for Dirac eigenvalues

Extended previous models to more complex supergravity theories

Abstract

We generalize previous works on the Dirac eigenvalues as dynamical variables of the Euclidean gravity and N=1 D=4 supergravity to on-shell N=2 D=4 Euclidean supergravity. The covariant phase space of the theory is defined as as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.