Related papers: Spectral action on noncommutative torus
We compute a Chern-Simons term induced by the fermions on noncommutative torus interacting with two U(1) gauge fields. For rational noncommutativity \theta \propto P/Q we find a new mixed term in the action which involves only those fields…
Formulas for the most general case of the zeta function associated to a quadratic+linear+constant form (in {\bf Z}) are given. As examples, the spectral zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to…
The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even dimension.
A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma model…
We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these metrics and study their spectral invariants obtained from the…
We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not…
We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space,…
This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of…
The definition of the spectral action involves the trace operator over states in the physical Hilbert space. We show that in the presence of chiral fermions there are consistency conditions on the fermionic representations. These conditions…
Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein gravity and Standard…
Witten constructed a topological quantum field theory with the Chern-Simons action as Lagrangian. We define a Chern-Simons action for 3-dimensional spectral triples. We prove gauge invariance of the Chern-Simons action, and we prove that it…
A Dirac operator is presented that will yield a 1+ summable regular even spectral triple for all noncommutative compact surfaces defined as subalgebras of the Toeplitz algebra. Connes' conditions for noncommutative spin geometries are…
We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the…
We construct the so-called theta vectors on noncommutative T^4, which correspond to the theta functions on commutative tori with complex structures. Following the method of Dieng and Schwarz, we first construct holomorphic connections and…
We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action…
Recently Dabrowski etc. \cite{DL} obtained the metric and Einstein functionals by two vector fields and Laplace-type operators over vector bundles, giving an interesting example of the spinor connection and square of the Dirac operator.…
In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple…
We prove sharp estimates in a shrinking target problem for the action of an arbitrary subgroup $\Gamma$ of $SL_2(\mathbb{Z})$ on the 2-torus. This can also be viewed as a non-commutative Diophantine approximation problem. The methods…
We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey-de Witt coefficients and make explicit calculations…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…