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Nonabelian strings in a dense matterJul 16 2007We consider gauge theories with scalar matter with and without supersymmetry at nonzero chemical potential. It is argued that a chemical potential plays a role similar to the FI term. We analyze theory at weak coupling regime at large chemical potential ... More

Integrability of the RG flows and the bulk/boundary correspondenceDec 31 1998We suggest that RG flows in the N=2 SUSY YM theories are governed by the pair of the integrable systems. The main dynamical ingredient amounts from the interaction of the small size instantons with the regulator degrees of freedom. The relation with the ... More

On a Casher-Banks relation in MQCDApr 02 1998We discuss the meaning of a Casher-Banks relation for the Dirac operator eigenvalues in MQCD. It suggests the interpretaion of the eigenvalue as a coordinate involved in the brane configuration.

Gauge Theories as String Theories: the First ResultsFeb 19 2006The brief review of the duality between gauge theories and closed strings propagating in the curved space is based on the lectures given at ITEP Winter School - 2005

Dualities in integrable systems and N=2 theoriesNov 05 1999We discuss dualities of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. It is shown that T duality in the string theory is related to the separation of variables procedure in dynamical system. We argue that there are analogues ... More

String/Gauge Correspondence; View from the High Energy SideSep 16 2002Jan 13 2003We briefly review the recent progress concerning the application of the hidden integrability to the derivation of the stringy/brane picture for the high energy QCD.

Instanton-torus knot duality in 5d SQED and $SU(2)$ SQCDApr 05 2016We 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.

Spontaneous Creation of the Brane World and Direction of the Time ArrowJun 08 2006In this note we consider the spontaneous creation of the brane world in five-dimensional space with nondynamical external four-form field via spherically asymmetric bounce solution. We argue that spherically asymmetric bounce suggests several inequivalent ... More

Angular Momentum and Gravimagnetization of the ${\cal N}=2$ SYM vacuumFeb 09 2011In this note we discuss the gravimagnetization of the ${\cal N}=2$ SYM vacuum in the $\Omega$-background. It is argued that the Seiberg-Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean $R^4$ space. The possible ... More

Konishi anomaly and N=1 effective superpotentials from matrix modelsOct 29 2002Oct 31 2002We discuss the restrictions imposed by the Konishi anomaly on the matrix model approach to the calculation of the effective superpotentials in N=1 SUSY gauge theories with different matter content. It is shown that they correspond to the anomaly deformed ... More

Spin Chains and Gauge/String DualityAug 27 2003Oct 09 2003The stringy picture behind the integrable spin chains governing the evolution equations in Yang-Mills theory is discussed. It is shown that one-loop dilatation operator in N=4 theory can be expressed in terms of two-point functions on 2d worldsheet. Using ... More

Low energy theorems and the Dirac operator spectral density in QCDDec 29 1998Mar 02 1999We discuss the behaviour of the spectral density of the massless Dirac operator at the small eigenvalues and quark masses compatible with the restrictions imposed by the low energy theorems in QCD. Sum rule for its derivative over the quark mass is found. ... More

Towards the low energy effective degrees of freedom in N=2 SUSY theories: branes and integrabilityAug 21 1998We discuss the brane interpretation of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. Degrees of freedom in the first integrable system responsible for the spectral Riemann surfaces comes from the hidden Higgs branch of the ... More

RG flows on the phase spaces and the $τ$ functions for the generic Hamiltonian systemsOct 10 2000Jan 29 2001We discuss the generic definition of the $\tau$ function for the arbitrary Hamiltonian system. The different approaches concerning the deformations of the curves and surfaces are compared. It is shown that the Baker-Akhiezer function for the secondary ... More

Semi-derived and derived Hall algebras for stable categoriesSep 24 2014Given a Frobenius category $\mathcal{F}$ satisfying certain finiteness conditions, we consider the localization of its Hall algebra $\mathcal{H(F)}$ at the classes of all projective-injective objects. We call it the {\it "semi-derived Hall algebra"} $\mathcal{SDH(F, ... More

One-loop derivation of the Wilson polygon - MHV amplitude dualityApr 02 2009We discuss the origin of the Wilson polygon - MHV amplitude duality at the perturbative level. It is shown that the duality for the MHV amplitudes at one-loop level can be proven upon the peculiar change of variables in Feynman parametrization and the ... More

Towards effective topological gauge theories on spectral curvesOct 30 1995Jan 22 1996We discuss a general approach to the nonperturbative treatment of quantum field theories based on existence of effective gauge theory on auxiliary ''spectral" Riemann curve. We propose an effective formulation for the exact solutions to some examples ... More

Testing Nonperturbative Orbifold ConjectureAug 09 2002We discuss Strassler's hypothesis of matching nonperturbative effects in orbifold pairs of gauge theories which are perturbatively planar equivalent. One of the examples considered is the parent N=1 SU(N) supersymmetric Yang-Mills theory and its nonsupersymmetric ... More

RG-Whitham dynamics and complex Hamiltonian systemsAug 02 2014Apr 07 2015Inspired 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 ... More

Baryon as dyonic instantonJun 20 2012Dec 04 2012We discuss the baryon in the holographic QCD framework and focus on the role of the bifundamental scalar field, realizing chiral symmetry breaking. We suggest the interpretation of a baryon as a dyonic instanton within the Atiyah-Manton-like approach ... More

Integrable Many-Body Systems and Gauge TheoriesNov 22 2000Dec 17 2000The review studies connections between integrable many-body systems and gauge theories. It is shown how the degrees of freedom in integrable systems are related with topological degrees of freedom in gauge theories. The relations between families of integrable ... More

Condensates and instanton - torus knot duality. Hidden Physics at UV scaleDec 29 2014Aug 16 2015We establish the duality between the torus knot superpolynomials or the Poincar\'e polynomials of the Khovanov homology and particular condensates in $\Omega$-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS) term. It is ... More

From Yang-Mills Lagrangian to MHV DiagramsOct 14 2005Jan 18 2006We prove the equivalence of a recently suggested MHV-formalism to the standard Yang-Mills theory. This is achieved by a formally non-local change of variables. In this note we present the explicit formulas while the detailed proofs are postponed to a ... More

Liouville theory and special coadjoint Virasoro orbitsNov 09 1993We describe the Hamiltonian reduction of the coajoint Kac-Moody orbits to the Virasoro coajoint orbits explicitly in terms of the Lagrangian approach for the Wess-Zumino-Novikov-Witten theory. While a relation of the coajoint Virasoro orbit $Diff \; S^1 ... More

Solutions to the reflection equation and integrable systems for N=2 SQCD with classical groupsFeb 03 1999Integrable systems underlying the Seiberg-Witten solutions for the N=2 SQCD with gauge groups SO(n) and Sp(n) are proposed. They are described by the inhomogeneous XXX spin chain with specific boundary conditions given by reflection matrices. We attribute ... More

Baryon and chiral symmetry breakingFeb 04 2014We 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 ... More

The CP(N-1) model on a Disc and Decay of a Non-Abelian StringJun 15 2013We 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. ... More

Aspects of the N=4 SYM amplitude -- Wilson polygon dualityNov 18 2009We discuss formulation of Wilson polygon - MHV amplitude duality at the perturbative level in various regularizations. For four gluons it is shown that at one loop one can formulate diagrammatic correspondence interpolating between the dimensional regularization ... More

More on the Tensorial Central Charges in N=1 Supersymmetric Gauge Theories (BPS Wall Junctions and Strings)Sep 03 1999Dec 29 1999We study the central extensions of the N=1 superalgebras relevant to the soliton solutions with the axial geometry - strings, wall junctions, etc. A general expression valid in any four-dimensional gauge theory is obtained. We prove that the only gauge ... More

Finite-size effects in exponential random graphs and cluster evaporationMay 08 2019In this Letter we find numerically the strong finite-size effects in the critical behavior of Erd\H{o}s-R\'enyi (ER) networks supplemented with chemical potentials for some motifs, in particular 2-stars and triangles. For the 2-star model above the critical ... More

Magnetic strings in Lattice QCD as Nonabelian VorticesJul 09 2007Lattice studies indicate existence of magnetic strings in QCD vacuum. We argue that recently found nonabelian strings with rich worldsheet dynamics provide a proper pattern for the strings observed on the lattice. In particular, within this pattern we ... More

Big Bang in $AdS_{5}$ with external field and flat 4d UniverseJun 06 2000Jul 06 2000We describe spontaneous creation of the Brane World in $AdS_{5}$ with external field. The resulting Brane World consists of a flat 4d spatially finite expanding Universe and curved expanding "regulator" branes. No negative tension branes are involved. ... More

On heavy states in supersymmetric gluodynamics at large NOct 28 1999It is argued that there are states (quasiparticles) with masses ranging over the scales $\Lambda N_{c}^{1/3} \div \Lambda N_{c}$ in N=1 supersymmetric multicolor gluodynamics. These states exist in the form of quantum bubbles made out of the BPS domain ... More

Hamiltonian systems of Calogero type and two dimensional Yang-Mills theoryApr 12 1993We obtain integral representations for the wave functions of Calogero-type systems,corresponding to the finite-dimentional Lie algebras,using exact evaluation of path integral.We generalize these systems to the case of the Kac-Moody algebras and observe ... More

RG limit cyclesFeb 11 2014In 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.

From effective actions to the background geometryNov 04 2004Jan 06 2005We discuss how the background geometry can be traced from the one-loop effective actions in nonsupersymmetric theories in the external abelian fields. It is shown that upon the proper identification of the Schwinger parameter the Heisenberg-Euler abelian ... More

Dualities in integrable systems: geometrical aspectsMar 01 2001We discuss geometrical aspects of different dualities in the integrable systems of the Hitchin type and its various generalizations. It is shown that T duality known in the string theory context is related to the separation of variables procedure in dynamical ... More

Tunneling into the Randall-Sundrum Brane WorldMay 08 2000May 23 2000We suggest a modification of the Randall-Sundrum scenario which doesn't involve branes with the negative tensions. In our scenario four-dimensional brane world is produced by the external field. The probability of this process is calculated and the physical ... More

Junctions and the Fate of Branes in External FieldsApr 06 1999Jan 03 2000We discuss the processes of brane bubble nucleation induced by the external branes. The quasiclassical solution for the nucleation by the single external brane has been found in the case when the brane junctions are possible. Exponential factor in the ... More

Spectral Degeneracy in Supersymmetric Gluodynamics and One-Flavor QCD related to N=1/2 SUSYOct 09 2004Nov 08 2004In supersymmetric gluodynamics (N=1 super-Yang-Mills theory) we show that the spectral functions induced by the nonchiral operator Tr G_{\alpha\beta} \bar\lambda^2 are fully degenerate in the J^{PC}=1^{\pm -} channels. The above operator is related to ... More

Anomalous Zero SoundJun 20 2012Jan 09 2013We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.

Remarks on Decay of Defects with Internal Degrees of FreedomJun 28 2010We consider the decay of metastable walls and strings populated by additional degrees of freedom. The examples involve the decay of an axion wall in an external magnetic field, pionic walls, metastable walls in dense QCD. It is shown that the induced ... More

Particle decay in false vacuumNov 08 2005We revisit the problem of decay of a metastable vacuum induced by the presence of a particle. For the bosons of the `master field' the problem is solved in any number of dimensions in terms of the spontaneous decay rate of the false vacuum, while for ... More

Anomalous QCD Contribution to the Debye Screening in an External Field via HolographyDec 07 2010Feb 15 2011In this paper we discuss the QCD contribution to the Abelian Debye and magnetic screening masses in a deconfined QCD plasma at finite temperature in the presence of an external magnetic field B. We use a holographic AdS/QCD setup in an AdS Schwarzschield ... More

An Exact Relation for N=1 Orientifold Field Theories with Arbitrary SuperpotentialApr 30 2004Oct 13 2004We discuss a nonperturbative relation for orientifold parent/daughter pairs of supersymmetric theories with an arbitrary tree-level superpotential. We show that super-Yang-Mills (SYM) theory with matter in the adjoint representation at N-->infinity, is ... More

SUSY field theories, integrable systems and their stringy/brane origin -- IIOct 30 1997Five and six dimensional SUSY gauge theories, with one or two compactified directions, are discussed. The 5d theories with the matter hypermultiplets in the fundamental representation are associated with the twisted $XXZ$ spin chain, while the group product ... More

Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- IJul 11 1997We discuss supersymmetric Yang-Mills theories with the multiple scales in the brane language. The issue concerns N=2 SUSY gauge theories with massive fundamental matter including the UV finite case of $n_{f}=2n_c$, theories involving products of SU(n) ... More

Deconfinement at the Argyres-Douglas point in SU(2) gauge theory with broken N=2 supersymmetryApr 12 2000Apr 19 2000We consider chiral condensates in SU(2) gauge theory with broken N=2 supersymmetry. The matter sector contains an adjoint multiplet and one fundamental flavor. Matter and gaugino condensates are determined by integrating out the adjoint field. The only ... More

High Energy QCD: Stringy Picture from Hidden IntegrabilityApr 22 2002We discuss the stringy properties of high-energy QCD using its hidden integrability in the Regge limit and on the light-cone. It is shown that multi-colour QCD in the Regge limit belongs to the same universality class as superconformal $\cal{N}$=2 SUSY ... More

Correlator of Wilson and t'Hooft Loops at Strong Coupling in $\mathcal{N}=4$ SYM TheoryApr 23 2009We calculate the correlator of a 't Hooft and a Wilson coplanar circular concentric loops at strong coupling in N=4 SYM theory when it reduces to the calculation of the composite minimal surface in the curved space with the proper boundary conditions. ... More

Spectrum of Quantum Transfer Matrices via Classical Many-Body SystemsOct 25 2013Dec 23 2013In 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 ... More

The Condensate from Torus KnotsJun 22 2015We discuss recently formulated instanton-torus knot duality in $\Omega$-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 ... More

Spontaneous Z2 Symmetry Breaking in the Orbifold Daughter of N=1 Super Yang-Mills Theory, Fractional Domain Walls and Vacuum StructureMay 03 2005Oct 19 2005We discuss the fate of the Z2 symmetry and the vacuum structure in an SU(N)xSU(N) gauge theory with one bifundamental Dirac fermion. This theory can be obtained from SU(2N) supersymmetric Yang--Mills (SYM) theory by virtue of Z2 orbifolding. We analyze ... More

Son-Yamamoto relation and Holographic RG flowsDec 01 2014Motivated 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 ... More

Baryon as dyonic instanton-II. Baryon mass versus chiral condensateSep 13 2013Oct 08 2013We 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 ... More

Revisiting the Faddeev-Skyrme Model and Hopf SolitonsJun 10 2013Jun 26 2013We 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" ... More

The Higgs and Coulomb/Confining Phases in "Twisted-Mass" Deformed CP(N-1) ModelDec 14 2005Jan 09 2006We consider non-supersymmetric two-dimensional CP(N-1) model deformed by a term presenting the bosonic part of the twisted mass deformation of N=2 supersymmetric version of the model. Our deformation has a special form preserving a Z_N symmetry at the ... More

Supersymmetric Quantum Chromodynamics: How Confined Non-Abelian Monopoles Emerge from Quark CondensationJan 05 2007Mar 10 2007We consider N =1 supersymmetric QCD with the gauge group U(N) and N_f=N quark flavors. To get rid of flat directions we add a meson superfield. The theory has no adjoint fields and, therefore, no 't Hooft-Polyakov monopoles in the quasiclassical limit. ... More

Confined Magnetic Monopoles in Dense QCDJan 06 2011Non-Abelian strings exist in the color-flavor locked phase of dense QCD. We show that kinks appearing in the world-sheet theory on these strings, in the form of the kink-antikink bound pairs, are the magnetic monopoles --- descendants of the 't Hooft-Polyakov ... More

Degenerations of Sklyanin algebra and Askey-Wilson polynomialsMar 04 1993A new trigonometric degeneration of the Sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied. A further contraction gives the standard quantum algebra $U_{q}(sl(2))$. It is ... More

Nonabelian Strings and AxionJan 18 2006We address two distinct but related issues: (i) the impact of (two-dimensional) axions in a two-dimensional theory known to model confinement, the CP(N-1) model; (ii) bulk axions in four-dimensional Yang-Mills theory supporting non-Abelian strings. In ... More

Non-Abelian Meissner Effect in Yang--Mills Theories at Weak CouplingDec 08 2004Feb 01 2005We present a weak-coupling Yang--Mills model supporting non-Abelian magnetic flux tubes and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux tubes are prototypes of the QCD strings. Dualizing the confined magnetic monopoles ... More

Holographic Hadro-QuarkoniumApr 14 2008May 28 2008We consider the recently suggested model for some resonances near the open charm threshold as bound states of charmonium inside excited light mesons. It is argued in the soft-wall holographic model of QCD that such states of heavy quarkonium necessarily ... More

Anomaly matching condition in two-dimensional systemsJan 31 2016Based 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 ... More

Critical behavior in topological ensemblesSep 11 2014Feb 11 2015We 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 $\Omega$ background and with 5D Chern-Simons term at the ... More

Flux-Tube Formation and Holographic TunnelingMay 06 2008We consider correlator of two concentric Wilson loops, a small and large ones related to the problem of flux-tube formation. There are three mechanisms which can contribute to the connected correlator and yield different dependences on the radius of the ... More

Hilbert Schemes, Separated Variables, and D-BranesJan 20 1999May 05 1999We explain Sklyanin's separation of variables in geometrical terms and construct it for Hitchin and Mukai integrable systems. We construct Hilbert schemes of points on $T^{*}\Sigma$ for $\Sigma = {\IC}, {\IC}^{*}$ or elliptic curve, and on ${\bf C}^{2}/{\Gamma}$ ... More

On the Deconstruction of TimeMar 03 2002Mar 11 2002In this note we discuss the possibility to get a time rather than space in the scenario of (de)construction of new dimension.

Non-Perturbative Production of Multi-Boson States and Quantum BubblesMay 06 1993The amplitude of production of $n$ on-mass-shell scalar bosons by a highly virtual field $\phi$ is considered in a $\lambda \phi^4$ theory with weak coupling $\lambda$ and spontaneously broken symmetry. The amplitude of this process is known to have an ... More

Integrability and Seiberg-Witten Exact SolutionMay 05 1995May 06 1995The exact Seiberg-Witten (SW) description of the light sector in the $N=2$ SUSY $4d$ Yang-Mills theory is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevsky (GP) solution to the elliptic Whitham equations. We consider this ... More

Quadruply-graded colored homology of knotsApr 11 2013We conjecture the existence of four independent gradings in the colored HOMFLY homology. We describe these gradings explicitly for the rectangular colored homology of torus knots and make qualitative predictions of various interesting structures and symmetries ... More

On third Poisson structure of KdV equationMar 02 1995The third Poisson structure of KdV equation in terms of canonical ``free fields'' and reduced WZNW model is discussed. We prove that it is ``diagonalized'' in the Lagrange variables which were used before in formulation of 2D gravity. We propose a quantum ... More

RG Equations from Whitham HierarchyFeb 02 1998Mar 02 1998The second derivatives of prepotential with respect to Whitham time-variables in the Seiberg-Witten theory are expressed in terms of Riemann theta-functions. These formulas give a direct transcendental generalization of algebraic ones for the Kontsevich ... More

Schwinger type processes via branes and their gravity dualsOct 19 2001Oct 30 2001We consider Schwinger type processes involving the creation of the charge and monopole pairs in the external fields and propose interpretation of these processes via corresponding brane configurations in Type IIB string theory. We suggest simple description ... More

N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_cMar 20 1996The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous) $sl(2)$ spin ... More

A Note on Spectral Curve for the Periodic Homogeneous $XYZ$-Spin ChainApr 15 1996We discuss the construction of the spectral curve and the action integrals for the ``elliptic" $XYZ$ spin chain of the length $N_c$. Our analysis can reflect the integrable structure behind the ``elliptic" ${\cal N}=2$ supersymmetric QCD with $N_f=2N_c$. ... More

More on the Tensor Response of the QCD Vacuum to an External Magnetic FieldJan 10 2012In 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 ... More

Is the Standard Model saved asymptotically by conformal symmetry?Sep 01 2014Oct 02 2014It 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. ... More

Phase transitions in social networks inspired by the Schelling modelJan 11 2018A generalized Schelling social segregation model is applied for the description of evolving social networks in which the number of connections of each agent (individual) remains approximately constant in time, though may be different for different agents. ... More

Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin AlgebrasNov 07 2001We consider the double-elliptic generalisation of dynamical systems of Calogero-Toda-Ruijsenaars type using finite-dimensional Mukai-Sklyanin algebras. The two-body system, which involves an elliptic dependence both on coordinates and momenta, is investigated ... More

A braid group action on parking functionsDec 02 2011Sep 20 2013We construct an action of the braid group on $n$ strands on the set of parking functions of $n$ cars such that elementary braids have orbits of length 2 or 3. The construction is motivated by a theorem of Lyashko and Looijenga stating that the number ... More

Vortical susceptibility of finite-density QCD matterJun 19 2016The 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 ... More

Logarithmic scaling in gauge/string correspondenceJan 16 2006Feb 01 2006We study anomalous dimensions of (super)conformal Wilson operators at weak and strong coupling making use of the integrability symmetry on both sides of the gauge/string correspondence and elucidate the origin of their single-logarithmic behavior for ... More

Gauge/string duality for QCD conformal operatorsApr 03 2003Renormalization group evolution of QCD composite light-cone operators, built from two and more quark and gluon fields, is responsible for the logarithmic scaling violations in diverse physical observables. We analyze spectra of anomalous dimensions of ... More

On the Chiral Magnetic Effect in Soft-Wall AdS/QCDMar 11 2010Jan 04 2011The essence of the chiral magnetic effect is generation of an electric current along an external magnetic field. Recently it has been studied by Rebhan et al. within the Sakai--Sugimoto model, where it was shown to be zero. As an alternative, we calculate ... More

On noncommutative vacua and noncommutative solitonsJul 31 2000Aug 22 2000We consider noncommutative theory of a compact scalar field. The recently discovered projector solitons are interpreted as classical vacua in the model considered. Localized solutions to the projector equation are pointed out and their brane interpretation ... More

Many-body localization and new critical phenomena in regular random graphs and constrained Erdős-Renyi networksNov 25 2016We consider from the localization perspective the new critical behavior discovered recently for the regular random graphs (RRG) and constrained Erd\H{o}s-Renyi networks (CERN). The diagonal disorder for standard models, we replace by the fugacity $\mu$ ... More

Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color NetworksMay 31 2015Nov 21 2015We have considered an equilibrium ensemble of large Erd\H{o}s-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 ... More

From elongated spanning trees to vicious random walksJun 14 2012Jun 25 2012Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are ... More

Dualities in Quantum Hall System and Noncommutative Chern-Simons TheoryNov 01 2001We discuss different dualities of QHE in the framework of the noncommutative Chern-Simons theory. First, we consider the Morita or T-duality transformation on the torus which maps the abelian noncommutative CS description of QHE on the torus into the ... More

Random ballistic growth and diffusion in symmetric spacesOct 16 2011Apr 27 2012Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N-column box is viewed a time-ordered product of N\times N-matrices consisting of a single sl_2-block which has a random position along the diagonal. We relate the ... More

Duality in Integrable Systems and Gauge TheoriesJun 29 1999Aug 25 2000We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as allow to construct ... More

Condensates near the Argyres-Douglas point in SU(2) gauge theory with broken N=2 supersymmetrySep 26 2000The behaviour of the chiral condensates in the SU(2) gauge theory with broken N=2 supersymmetry is reviewed. The calculation of monopole, dyon, and charge condensates is described. It is shown that the monopole and charge condensates vanish at the Argyres-Douglas ... More

Integrable many-body problems from the field theoriesOct 29 1994We review recent results which clarify the role of the integrable many-body problems in the quantum field theory framework.They describe the dynamics of the topological degrees of freedom in the theories which are obtained by perturbing the topological ... More

Arc spaces and DAHA representationsOct 07 2011Dec 02 2011A theorem of Y. Berest, P. Etingof and V. Ginzburg states that finite dimensional irreducible representations of a type A rational Cherednik algebra are classified by one rational number m/n. Every such representation is a representation of the symmetric ... More

Symmetries of some motivic integralsApr 05 2008We give an explicit formula for the motivic integrals related to the Milnor number over spaces of parametrised arcs on the plane with fixed tangency orders with the axis. These integrals are rational functions of the parameters and the class of the affine ... More

q,t-Catalan numbers and knot homologyMar 03 2010Oct 07 2011We propose an algebraic model of the conjectural triply graded homology of Gukov, Dunfield and Rasmussen for some torus knots. It turns out to be related to the q,t-Catalan numbers of Garsia and Haiman.

On divisorial filtrations on sheavesFeb 17 2005A notion of Poincar\'e series was introduced by A.Campillo et al. It was developed by Delgado and Gusein-Zade for a multi-index filtration corresponding to the sequence of blow-ups. The present paper suggests the way to generalize the notion of Poincar\'e ... More

Branes and integrability in the N=2 SUSY YM theoryDec 26 1996Sep 05 1997We suggest the brane interpretation of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. Degrees of freedom of the Calogero type integrable system responsible for the appearance of the spectral Riemann surfaces originate from ... More

On the $S_n$-equivariant Euler characteristic of moduli spaces of hyperelliptic curvesApr 18 2008The generating function for $S_n$-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g>1 is calculated. This answer generalizes the known ones for genera 2 and 3 and answers obtained by J. Bergstrom for any ... More