It has been recently shown by Landi and Rovelli that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possibility that the eigenvalues of the Dirac operator might play the same role in the case of supergravity. It is shown that to this end some constraints on covariant phase space as well as on the e...

The spectral flow of the low-lying eigenvalues of the improved and unimproved Wilson-Dirac operator is studied on instanton-like configurations and on thermalized quenched configurations at various β-values and lattice sizes. We also investigate the space-time localisation and chirality of the corresponding eigenvectors.

In this paper we consider Γ → M̃ → M , a Galois covering with boundary and D̃/, a Γ-invariant generalized Dirac operator on M̃ . We assume that the group Γ is of polynomial growth with respect to a word metric. By employing the notion of noncommutative spectral section associated to the boundary operator D̃/0 and the b-calculus on Galois coverings with boundary, we develop a higher Atiyah-PatodiSin...

The overlap Dirac operator, derived from the overlap formalism for the special case of vector gauge theories, is a way to realize exact chiral symmetry on the lattice. Exact chiral symmetry on the lattice does come at a price – numerical implementation of the overlap Dirac operator is significantly more expensive than Wilson or staggered operator. In spite of this numerical hurdle, we already h...

Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...

We compute the spectral action of SU(2)/Γ with the trivial spin structure and the round metric and find it in each case to be equal to 1 |Γ| ( Λf̂ (0)− 1 4 Λf̂(0) ) +O(Λ). We do this by explicitly computing the spectrum of the Dirac operator for SU(2)/Γ equipped with the trivial spin structure and a selection of metrics. Here Γ is a finite subgroup of SU(2). In the case where Γ is cyclic, or dicy...

We compute the axial anomaly for the Taub-NUT metric on R. We show that the axial anomaly for the generalized Taub-NUT metrics introduced by Iwai and Katayama is finite, although the Dirac operator is not Fredholm. We show that the essential spectrum of the Dirac operator is the whole real line. Pacs: 04.62.+v

We present a derivation of the general form of the scalar potential in Yang-Mills theory of a non-commutative space which is a product of a four-dimensional manifold times a discrete set of points. We show that a non-trivial potential without flat directions is obtained after eliminating the auxiliary fields only if constraints are imposed on the mass matrices utilised in the Dirac operator. Th...

We show that for generic Riemannian metrics on a closed spin manifold of dimension three the Dirac operator has only simple eigenvalues.