v 1 1 4 Ju l 1 99 7 Observables of the Euclidean Supergravity

ar X iv : g r - qc / 9 80 70 11 v 1 6 J ul 1 99 8 Constraints on spacetime manifold in Euclidean supergravity in terms of Dirac eigenvalues

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 addmits Dirac eigenvalues as observables, are derived. Typeset using REVTEX

M ar 2 00 8 On the Dirac Eigenvalues as Observables of the on - shell N = 2 D = 4 Euclidean Supergravity

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 v...

1 Observables of D = 4 Euclidean Supergravity and Dirac

The observables of supergravity are defined to be the phase space gauge invariant objects of the theory. Dirac eigenvalues are obsevables of Euclidean gravity on a compact manifold [1,2,3]. We resume the basic results for super-gravity [4,5], [6,7]. The general setting which we consider is of minimal supergravity in four dimensions on a compact spin manifold without boundary endowed with an Euc...

ar X iv : h ep - t h / 96 07 19 7 v 1 2 5 Ju l 1 99 6 DSF preprint 96 / 36 NON - LOCAL BOUNDARY CONDITIONS FOR MASSLESS SPIN - 12 FIELDS

This paper studies the 1-loop approximation for a massless spin-1/2 field on a flat four-dimensional Euclidean background bounded by two concentric 3-spheres, when non-local boundary conditions of the spectral type are imposed. The use of ζ-function regularization shows that the conformal anomaly vanishes, as in the case when the same field is subject to local boundary conditions involving proj...

ar X iv : h ep - t h / 96 07 09 3 v 1 1 2 Ju l 1 99 6 Quantum dynamics of N = 1 , D = 4 supergravity compensator