On the symplectic two-form of gravity in terms of Dirac eigenvalues

A spectral action of Euclidean supergravity is proposed. We calculate up to $a_4$, the Seeley-Dewitt coefficients in the expansion of the spectral action associated to the supergravity Dirac operator. This is possible because in simple supergravity, as in pure gravity, a well defined and mathematically consistent Dirac operator can be constructed.

Toward Supergravity Spectral Action

A spectral action for a generalized bosonic sector corresponding to the Dirac operator of Euclidean supergravity is proposed. We calculate, up to a4, the Seeley–DeWitt coefficients in the expansion of the spectral action. It is in general not known how to construct a "matter fermionic" supersymmetric partner to the spectral action. The action we propose provides the effective action to be completed to get, at any order of the expansion, the corresponding supersymmetric action.

Toward a supergravity spectral action

We generalize previous works on the Dirac eigenvalues as dynamical variables of 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 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.

On the Dirac eigenvalues as observables of the on-shell N = 2D = 4 Euclidean supergravity

We generalize a 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 space–time manifold, under which space–time admits Dirac eigenvalues as observables, are derived.

C. Ciuhu

Papers

Constraints on space–time manifold in euclidean supergravity in terms of dirac eigenvalues