Related papers: Spectral action beyond the weak-field approximatio…

We study the heterotic string compactified on K3 x T^2 near the line T=U, where the effective action becomes singular due to an SU(2) gauge symmetry enhancement. By `integrating in' the light W^\pm vector multiplets we derive a quantum…

We investigate the quantum aspects of a charged hypermultiplet in deformed N=(1,1) superspace with singlet non-anticommutative deformation of supersymmetry. This model is a "star" modification of the hypermultiplet interacting with a…

For totally ergodic Z^2-actions a collection of weak limits provide the set {2,4, ..., 2 ^ n} of spectral multiplicities for their tensor product. Our conditions allow to obtain a similar result for mixing actions via some limit procedure.

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…

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave…

We present a first numerical investigation of a non-commutative gauge theory defined via the spectral action for Moyal space with harmonic propagation. This action is approximated by finite matrices. Using Monte Carlo simulation we study…

The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.

We propose a construction for spectral triple on algebras associated with subshifts. One-dimensional subshifts provide concrete examples Z-actions on Cantor sets. The C*-algebra of this dynamical system is generated by functions in C(X) and…

The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of…

For a symplectic isotopy on the two-dimensional disc we show that the classical spectral invariants of Viterbo [20] can be extended in a meaningful way to {\it non-compactly} supported Hamiltonians. We establish some basic properties of…

Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space, let M(T) denote the set of essential values of the spectral multiplicity function of the Koopman unitary…

We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order…

The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have…

We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the…

We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 space-time dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators…

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…

We discuss the possibility to extend the spectral action up to energy close to the Planck scale, taking also into account the gravitational effects given by graviton exchange. Including this contribution in the theory, the coupling constant…

We construct a `non-unital spectral triple of finite volume' out of the Moyal product and a differential square root of the harmonic oscillator Hamiltonian. We find that the spectral dimension of this triple is d but the KO-dimension is 2d.…

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that…