A classification of Hermitian representations for the recently introduced fuzzy torus algebra is presented. This is carried out by regarding the fuzzy torus algebra as a q-deformation of parafermion. In addition to the known representations, new representations of both finite and infinite dimension are found. Using the infinite dimensional representation, coherent state for the fuzzy torus is c...

We prove a families version of the index theorem for operators generalizing those studied by C. Callias and later by N. Anghel, which are operators on a manifold with boundary having the form D + iΦ, where D is elliptic pseudodifferential with self-adjoint symbols, and Φ is a self-adjoint bundle endomorphism which is invertible at the boundary and commutes with the symbol of D there. The index ...

The recently developed families index theory for the overlap lattice Dirac operator is applied to demonstrate an interplay between topological features of the space of SU(N) lattice gauge fields on the 4-torus and the existence question for G0 gauge fixings which do not have the Gribov problem. The continuum version of our considerations leads to topological obstructions to the existence of suc...

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.

We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a stringmanifold is a per-Hilbert–Schmidt locally equivalent co-spin manifold and thus admits a Dirac operator.

We compute the ratio ΛL/ΛMS between the scale parameter ΛL, associated with a lattice formulation of QCD using the overlap-Dirac operator, and ΛMS of the MS renormalization scheme. To this end, the necessary one-loop relation between the lattice coupling g0 and the coupling renormalized in the MS scheme is calculated, using the lattice background field technique.

Let N be a closed connected spin manifold admitting one metric of positive scalar curvature. In this paper we use the higher eta-invariant associated to the Dirac operator on N in order to distinguish metrics of positive scalar curvature on N . In particular, we give sufficient conditions, involving π1(N) and dim N , for N to admit an infinite number of metrics of positive scalar curvature that...

We show that theAtiyah–Patodi–Singer reducedη-invariant of the twisted Dirac operator on a closed 4m− 1-dimensional spin manifold, with the twisted bundle being the Witten bundle appearing in the theory of elliptic genus, is a meromorphic modular form of weight 2m up to an integral q-series. We prove this result by combining our construction of certain modular characteristic forms associated to...

In this note we show that every compact spin manifold of dimension ≥ 3 can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity 1.

We use the spectra of Dirac type operators on the sphere S to produce sharp L inequalities on the sphere. These operators include the Dirac operator on S, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in R.