arXiv subjects

A. Gorsky

Publications and source records attributed to A. Gorsky.

At least 37 records · Page 2Linked to original sources

arXiv2017

Finite plateau in spectral gap of polychromatic constrained random networks

We consider the canonical ensemble of multilayered constrained Erdos-Renyi networks (CERN) and regular random graphs (RRG), where each layer represents graph vertices painted in a specific color. We study the critical behavior in such networks under changing the fugacity, $μ$, which controls the number of monochromatic triads of nodes. The behavior of considered systems is investigated via the spectral properties of the adjacency and Laplacian matrices of corresponding networks. For some wide region of $μ$ we find the formation of a finite plateau in the number of the intercolor links, which exactly matches the finite plateau for the algebraic connectivity of the network (the value of the first non-vanishing eigenvalue of the Laplacian matrix, $λ_2$). We claim that at the plateau the restoring of the spontaneously broken $Z_2$ symmetry by the mechanism of modes collectivization in clusters of different colors occurs. The phenomena of a finite plateau formation holds for the polychromatic (multilayer) networks with $M>2$ colors.

cond-mat.stat-mech↗

arXiv2016

Eigenvalue tunnelling and decay of quenched random networks

We consider the canonical ensemble of $N$-vertex Erdős-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity $μ$ for each closed triple of bonds. We claim complete defragmentation of large-$N$ graphs into the collection of $[p^{-1}]$ almost full subgraphs (cliques) above critical fugacity, $μ_c$, where $p$ is the ER bond formation probability. Evolution of the spectral density, $ρ(λ)$, of the adjacency matrix with increasing $μ$ leads to the formation of two-zonal support for $μ>μ_c$. Eigenvalue tunneling from one (central) zone to the other means formation of a new clique in the defragmentation process. The adjacency matrix of the ground state of a network has the block-diagonal form where number of vertices in blocks fluctuate around the mean value $Np$. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.

cond-mat.stat-mech↗

arXiv2016

Vortical susceptibility of finite-density QCD matter

The susceptibility of finite-density QCD matter to vorticity is introduced, as an analog of magnetic susceptibility. It describes the spin polarization of quarks and antiquarks in finite-density QCD matter induced by rotation. We estimate this quantity in the chirally broken phase using the mixed gauge-gravity anomaly at finite baryon density. It is proposed that the vortical susceptibility of QCD matter is responsible for the polarization of $Λ$ and ${\bar Λ}$ hyperons observed recently in heavy ion collisions at RHIC by the STAR Collaboration.

hep-ph↗

arXiv2016

Instanton-torus knot duality in 5d SQED and $SU(2)$ SQCD

We briefly review the instanton-torus knot duality found in 5d SUSY gauge theories with one compact dimension. The fermion condensate turn out to be the generating function for the torus knot polynomials colored by the fundamental representation.

hep-th↗

arXiv2016

Anomaly matching condition in two-dimensional systems

Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\rm QCD}_4$, we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with diagonal vector and axial current two-point functions. Being fully non-perturbative, this relation may be regarded as anomaly matching for conductivities or certain transport coefficients depending on the system. We consider the holographic RG flows in holographic Yang-Mills-Chern-Simons theory via the Hamilton-Jacobi equation with respect to the radial coordinate. Within this holographic model it is found that the RG flows for the following relations are diagonal: Son-Yamamoto relation and the left-right polarization operator. Thus the Son-Yamamoto relation holds at wide range of energy scales.

hep-th↗

arXiv2015

Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks

We have considered an equilibrium ensemble of large Erdős-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability, $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples, $μ$. Minimizing the system energy, we see for some positive $μ$ formation of two predominantly unicolor clusters, linked by a "string" of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in emergence of a wide plateau on the $N_{bw}(μ)$-curve, which is relevant to a spinodal decomposition in 1st order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby-universes in 2D gravity. We have conjectured that observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

cond-mat.stat-mech↗

arXiv2015

Condensates and instanton - torus knot duality. Hidden Physics at UV scale

We establish the duality between the torus knot superpolynomials or the Poincaré polynomials of the Khovanov homology and particular condensates in $Ω$-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS) term. It is explicitly shown that $n$-instanton contribution to the condensate of the massless flavor in the background of four-observable, exactly coincides with the superpolynomial of the $T(n,nk+1)$ torus knot where $k$ - is the level of CS term. In contrast to the previously known results, the particular torus knot corresponds not to the partition function of the gauge theory but to the particular instanton contribution and summation over the knots has to be performed in order to obtain the complete answer. The instantons are sitting almost at the top of each other and the physics of the "fat point" where the UV degrees of freedom are slaved with point-like instantons turns out to be quite rich. Also also see knot polynomials in the quantum mechanics on the instanton moduli space. We consider the different limits of this correspondence focusing at their physical interpretation and compare the algebraic structures at the both sides of the correspondence. Using the AGT correspondence, we establish a connection between superpolynomials for unknots and q-deformed DOZZ factors.

hep-th↗

arXiv2015

The Condensate from Torus Knots

We discuss recently formulated instanton-torus knot duality in $Ω$-deformed 5D SQED on $\mathbb{R}^4 \times S^1$ focusing at the microscopic aspects of the condensate formation in the instanton ensemble. Using the chain of dualities and geometric transitions we embed the SQED with a surface defect into the $SU(2)$ SQCD with $N_f=4$ and identify the numbers $(n,m)$ of the torus $T_{n,m}$ knot as instanton charge and electric charge. The HOMFLY torus knot invariants in the fundamental representation provide entropic factor in the condensate of the massless flavor counting the degeneracy of the instanton--W-boson web with instanton and electric numbers $(n,m)$ but different spin and flavor content. Using the inverse geometrical transition we explain how our approach is related to the evaluation of the HOMFLY invariants in terms of Wilson loop in 3d CS theory. The reduction to 4D theory is briefly considered and some analogy with baryon vertex is conjectured.

hep-th↗

arXiv2015

RG-Whitham dynamics and complex Hamiltonian systems

Inspired by the Seiberg-Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group(RG)-like Whitham behavior. We show that at the Argyres-Douglas(AD) point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne-Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Omega - deformed theory.

hep-th↗

arXiv2015

Critical behavior in topological ensembles

We consider the relation between three physical problems: 2D directed lattice random walks, ensembles of $T_{n,n+1}$ torus knots, and instanton ensembles in 5D SQED with one compact dimension in $Ω$ background and with 5D Chern-Simons term at the level one. All these ensembles exhibit the critical behavior typical for the "area+length+corners" statistics of grand ensembles of 2D directed paths. Using the combinatorial description, we obtain an explicit expression of the generating function for $q$-Narayana numbers which amounts to the new critical behavior in the ensemble of $T_{n,n+1}$ torus knots and in the ensemble of instantons in 5D SQED. Depending on the number of the nontrivial fugacities, we get either the critical point, or cascade of critical lines and critical surfaces. In the 5D gauge theory the phase transition is of the 3rd order, while in the ensemble of paths and ensemble of knots it is typically of the 1st order. We also discuss the relation with the integrable models.

hep-th↗

arXiv2014

Son-Yamamoto relation and Holographic RG flows

Motivated by the Son-Yamamoto (SY) relation which connects the three point and two-point correlators we consider the holographic RG flows in the bottom-up approach to holographic QCD via the Hamilton-Jacobi (HJ) equation with respect to the radial coordinate . It is shown that the SY relation is diagonal with respect to the RG flow in the 5d YM-CS model while the RG equation acquires the inhomogeneous term in the model with the additional scalar field which encodes the chiral condensate.

hep-th↗

arXiv2014

Is the Standard Model saved asymptotically by conformal symmetry?

It is pointed out that the top-quark and Higgs masses and the Higgs VEV satisfy with great accuracy the relations 4m_H^2=2m_T^2=v^2, which are very special and reminiscent of analogous ones at Argyres - Douglas points with enhanced conformal symmetry. Furthermore, the RG evolution of the corresponding Higgs self-interaction and Yukawa couplings λ(0)=1/8 and y(0)=1 leads to the free-field stable point λ(M_Pl)= \dot λ(M_Pl)=0 in the pure scalar sector at the Planck scale, also suggesting enhanced conformal symmetry. Thus, it is conceivable that the Standard Model is the low-energy limit of a distinct special theory with (super?) conformal symmetry at the Planck scale. In the context of such a "scenario" one may further speculate that the Higgs particle is the Goldstone boson of (partly) spontaneously broken conformal symmetry. This would simultaneously resolve the hierarchy and Landau pole problems in the scalar sector and would provide a nearly flat potential with two almost degenerate minima at the electroweak and Planck scales.

hep-ph↗

arXiv2014

RG limit cycles

In this review we consider the concept of limit cycles in the renormalization group flows. The examples of this phenomena in the quantum mechanics and field theory will be presented.

hep-th↗

arXiv2014

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.

hep-ph↗

arXiv2013

Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems

In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous ${\mathfrak g}{\mathfrak l}_n$-invariant XXX spin chain on $N$ sites with twisted boundary conditions can be found in terms of velocities of particles in the rational $N$-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all $N$ particles and the other one is an $N$-dimensional Lagrangian submanifold obtained by fixing levels of $N$ classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the ${\mathfrak g}{\mathfrak l}_n$ Gaudin model with $N$ marked points (on the quantum side) and the Calogero-Moser system with $N$ particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.

hep-th↗

arXiv2013

Baryon as dyonic instanton-II. Baryon mass versus chiral condensate

We discuss the description of baryon as the dyonic instanton in holographic QCD. The solution generalizes the Skyrmion taking into account the infinite tower of vector and axial mesons as well as the chiral condensate. We construct the solution with unit baryon charge and study the dependence of its mass on the chiral condensate. The elegant explanation of the Ioffe's formula has been found and we speculate on the relation between physical scales of the chiral and conformal symmetry breaking.

hep-th↗

arXiv2013

Revisiting the Faddeev-Skyrme Model and Hopf Solitons

We observe that the Faddeev-Skyrme model emerges as a low-energy limit of scalar QED with two charged scalar fields and a selfinteraction potential of a special form (inspired by supersymmetric QCD). Then we discuss possible Hopf solitons of the "twisted-toroidal" type.

hep-th↗

arXiv2013

The CP(N-1) model on a Disc and Decay of a Non-Abelian String

We consider the role of quantum effects in the non-perturbative decay of non-abelian string with orientational moduli in non-supersymmetric D=4 gauge theory. To this aim the effective action in the $CP(N-1)$ model on a disc at large N has been calculated. It exhibits phase transition at some radius, the "wrong sign" Luscher term and large boundary boojum-like negative contribution. The effect of $θ$ - term and the possibility of the spontaneous creation of the non-abelian string are briefly discussed.

hep-th↗