18 research outputs found
Spectral action, Weyl anomaly and the Higgs-Dilaton potential
We show how the bosonic spectral action emerges from the fermionic action by
the renormalization group flow in the presence of a dilaton and the Weyl
anomaly. The induced action comes out to be basically the Chamseddine-Connes
spectral action introduced in the context of noncommutative geometry. The
entire spectral action describes gauge and Higgs fields coupled with gravity.
We then consider the effective potential and show, that it has the desired
features of a broken and an unbroken phase, with the roll down.Comment: 23 pages, 4 figure
Matrix geometries and Matrix Models
We study a two parameter single trace 3-matrix model with SO(3) global
symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase.
Configurations in the matrix phase are consistent with fluctuations around a
background of commuting matrices whose eigenvalues are confined to the interior
of a ball of radius R=2.0. We study the co-existence curve of the model and
find evidence that it has two distinct portions one with a discontinuous
internal energy yet critical fluctuations of the specific heat but only on the
low temperature side of the transition and the other portion has a continuous
internal energy with a discontinuous specific heat of finite jump. We study in
detail the eigenvalue distributions of different observables.Comment: 20 page
Motives and periods in Bianchi IX gravity models
In this paper we show that the heat coefficients of the Dirac-Laplacian of SU(2)-invariant Bianchi IX metrics are periods of motives of complements in affine spaces of unions of quadrics and hyperplanes
The topological Bloch-Floquet transform and some applications
Some relevant transport properties of solids do not depend only on the spectrum of the electronic Hamiltonian, but on finer properties preserved only by unitary equivalence, the most striking example being the conductance. When interested in such properties, and aiming to a simpler model, it is mandatory to check that the simpler effective Hamiltonian is approximately unitarily equivalent to the original one, in the appropriate asymptotic regime. In this paper, we consider the Hamiltonian of an electron in a 2-dimensional periodic potential (e.g. generated by the ionic cores of a crystalline solid) under the influence of a uniform transverse magnetic field. We prove that such Hamiltonian is approximately unitarily equivalent to a Hofstadter-like (resp. Harper-like) Hamiltonian, in the limit of weak (resp. strong) magnetic field. The result concerning the case of weak magnetic field holds true in any dimension. Finally, in the limit of strong uniform magnetic field, we show that an additional periodic magnetic potential induces a non-trivial coupling of the Landau bands
Rationality of spectral action for Robertson-Walker metrics
We use parametric pseudodifferential calculus to prove a conjecture by A. Connes and A. Chamseddine: we show that each term in the heat kernel expansion of the Dirac-Laplacian of a Robertson-Walker metric is described a several variable polynomial with rational coefficients