Related papers: Spectral action, Weyl anomaly and the Higgs-Dilato…

Starting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another…

In this letter we calculate the full Higgs-Dilaton action describing the Weyl anomaly using the bosonic spectral action. This completes the work we started in our previous paper (JHEP 1110 (2011) 001). We also clarify some issues related to…

We show how (a slight modification of) the noncommutative geometry bosonic spectral action can be obtained by the cancelation of the scale anomaly of the fermionic action. In this sense the standard model coupled with gravity is induced by…

We consider both the bosonic and fermionic second quantization of spectral triples in the presence of a chemical potential. We show that the von Neumann entropy and the average energy of the Gibbs state defined by the bosonic and fermionic…

We propose that the fermionic part of the action in the framework of the noncommutative description of the Standard Model is spectral, in an analogous way to the bosonic part of the action that is customary considered as being spectral. We…

The presence of chiral fermions in the physical Hilbert space implies consistency conditions on the spectral action. These conditions are equivalent to the absence of gauge and gravitational anomalies. Suggestions for the fermionic part of…

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…

We show, in the case of a U(1)L spontaneously broken gauge theory, how introducing a composite Wess-Zumino field, with a derivative coupling to the fermionic current, and a composite scalar sector leads to infinitely massive quarks and…

The arbitrary mass scale in the spectral action for the Dirac operator in the spectral action is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms in the spectral action and determine the dilaton couplings.…

Chamseddine and Connes have argued that the action for Einstein gravity, coupled to the SU(3)\times SU(2)\times U(1) standard model of particle physics, may be elegantly recast as the "spectral action" on a certain "non-commutative…

We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition…

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…

A proposal that the bosonic action of gravity and the standard model is induced from the fermionic action is investigated. It is suggested that this might occur naturally in state sum models.

In this publication we present an extension of the Standard Model within the framework of Connes' noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] which contains the Standard Model particles,…

Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the…

We consider aspects of the noncommutative approach to the standard model based on the spectral action principle. We show that as a consequence of the incorporation of the Clifford structures in the formalism, the spectral action contains an…

We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…

We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective…

Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix…

Recently, it has been pointed out that dimensionless actions in four dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed {\it restricted Weyl…