Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces

We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.Comment: Latex, 10 page

Renormalization group-like proof of the universality of the Tutte polynomial for matroids

In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions of some differential equations which are of the same type as the differential equations used to describe the renormalization group flow in quantum field theory. This approach allows us to also prove, in a different way, a matroid Tutte polynomial convolution formula published by Kook, Reiner and Stanton (1999). This FPSAC contribution is an extended abstract.Comment: 12 pages, 3 figures, conference proceedings, 25th International Conference on Formal Power Series and Algebraic Combinatorics, Paris, France, June 201

Location and Direction Dependent Effects in Collider Physics from Noncommutativity

We examine the leading order noncommutative corrections to the differential and total cross sections for e+ e- --> q q-bar. After averaging over the earth's rotation, the results depend on the latitude for the collider, as well as the direction of the incoming beam. They also depend on scale and direction of the noncommutativity. Using data from LEP, we exclude regions in the parameter space spanned by the noncommutative scale and angle relative to the earth's axis. We also investigate possible implications for phenomenology at the future International Linear Collider.Comment: version to appear in PR

The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model

We study the form factors appearing in the inclusive decay b -> s g^*, in the framework of the noncommutative standard model. Here g^* denotes the virtual gluon. We get additional structures and the corresponding form factors in the noncommutative geometry. We analyse the dependencies of the form factors to the parameter p\Theta k where p (k) are the four momenta of incoming (outgoing) b quark (virtual gluon g^*, \Theta is a parameter which measures the noncommutativity of the geometry. We see that the form factors are weaklyComment: 8 pages, 7 figure

Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets

We will present a new extension of the standard model of particle physics in its almostcommutative formulation. This extension has as its basis the algebra of the standard model with four summands [11], and enlarges only the particle content by an arbitrary number of generations of left-right symmetric doublets which couple vectorially to the U(1)_YxSU(2)_w subgroup of the standard model. As in the model presented in [8], which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section

Non-commutative spaces in physics and mathematics

The present review aims both to offer some motivations and mathematical prerequisites for a study of NCG from the viewpoint of a theoretical physicist and to show a few applications to matrix theory and results obtained. Lectures given by the author at the TMR School on contemporary string theory and brane physics, 26 Jan--2 Feb 2000, Torino.Comment: 27 pages + figures (in .eps format), first part appeared as hep-th/9802129. submitted to Class. Quant. Gra

EPRL/FK Group Field Theory

The purpose of this short note is to clarify the Group Field Theory vertex and propagators corresponding to the EPRL/FK spin foam models and to detail the subtraction of leading divergences of the model.Comment: 20 pages, 2 figure

An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited