Uniform infinite planar triangulation and related time-reversed critical branching process

We establish a connection between the uniform infinite planar triangulation and some critical time-reversed branching process. This allows to find a scaling limit for the principal boundary component of a ball of radius R for large R (i.e. for a boundary component separating the ball from infinity). We show also that outside of R-ball a contour exists that has length linear in R.Comment: 27 pages, 5 figures, LaTe

Holographic fermions at strong translational symmetry breaking: a Bianchi-VII case study

It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion response computed by the emergent quantum critical IR, even when the potential becomes relevant in the infra-red. However, in the regime where holographic quasi-particles occur, defining a Fermi surface in the continuum, they acquire a finite lifetime at any finite potential strength. At the transition from irrelevancy to relevancy of the Bianchi potential in the deep infra-red the quasi-particle remnants disappear completely and the fermion spectrum exhibits a purely relaxational behaviour.Comment: 30 pages, 10 figure

Baryon and chiral symmetry breaking

We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe's formula for the baryon mass.Comment: 7 pages, Contribution to the Proceedings of the II Russian-Spanish Congress "Particle and Nuclear Physics at all Scales and Cosmology", Saint-Petersburg, October 1-4, 201

Four-point correlator of vector currents and electric current susceptibility in holographic QCD

In this work we calculate the four-point correlation function of vector quark currents of QCD via holographic QCD model. Computing the correlator we take into account the exchange of vector and axial vector bosons and dilaton in the bulk. The result is used for calculation of the two-point correlator of electromagnetic currents in external magnetic field at zero momentum, related to RHIC experiments, chiral magnetic effect and lattice study. At zero temperature we find this quantity to be loosely connected with chiral symmetry breaking and strongly dependent on the confinement properties. Some features of the AdS/QCD models are also discussed.Comment: 14 pages, 1 figure (v2: references added, typos corrected

More on the Tensor Response of the QCD Vacuum to an External Magnetic Field

In this Letter we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto (SY) anomaly matching equation. It is shown that the SY relation in the IR implies a nontrivial interplay between the kinetic and WZW terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.Comment: 20 pages, 2 figure

Wilson loops in holographic models with a gluon condensate

The aim of this work is to study the holographic dual to the gauge theory with a nonzero gluon condensate. We check for consistency the holographic way of describing the condensate and calculate the expectation value of a small Wilson loop in the presence of the gluon condensate, thus obtaining the relevant coefficient in the operator product expansion of the small loop in different holographic models. We also study the effect of the condensate on the Gross-Ooguri phase transition in the correlator of two circular Wilson loops in parallel and concentric configurations. In the numerical study of the concentric case, we find that the phase transition changes its order when the size of the loops is of order of the gluon condensate. We report this change of the phase transition order to be a new effect in Wilson loop correlators.Comment: 24 pages, 6 figure

Genetic determinants of complicated pregnancy

The connections of polymorphic variants of the gene of vasoactive hormones with the level of arterial pressure in pregnant women, depending on the development of preeclampsia (PE), have been studie