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Open intersection numbers and free fieldsJun 21 2016Jul 05 2016A complete set of the Virasoro and W-constraints for the Kontsevich-Penner model, which conjecturally describes intersections on moduli spaces of open curves, was derived in our previous work. Here we show that these constraints can be described in terms ... More

Cut-and-join description of generalized Brezin-Gross-Witten modelAug 04 2016Aug 17 2016We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro constraints, which completely specify ... More

Open intersection numbers, Kontsevich-Penner model and cut-and-join operatorsDec 11 2014Jun 22 2016We continue our investigation of the Kontsevich--Penner model, which describes intersection theory on moduli spaces both for open and closed curves. In particular, we show how Buryak's residue formula, which connects two generating functions of intersection ... More

Cut-and-join description of generalized Brezin-Gross-Witten modelAug 04 2016Dec 29 2018We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro constraints, which completely specify ... More

Matrix integral expansion of colored Jones polynomials for figure-eight knotNov 20 2014In this note we examine a possible extension of the matrix integral representation of knot invariants beyond the class of torus knots. In particular, we study a representation of the SU(2) quantum Racah coefficients by double matrix integrals. We find ... More

Free fermions and tau-functionsDec 25 2012Sep 24 2013We review the formalism of free fermions used for construction of tau-functions of classical integrable hierarchies and give a detailed derivation of group-like properties of the normally ordered exponents, transformations between different normal orderings, ... More

Continuous deformations of polyhedra that do not alter the dihedral anglesDec 19 2012Jan 03 2013We prove that, both in the hyperbolic and spherical 3-spaces, there exist nonconvex compact boundary-free polyhedral surfaces without selfintersections which admit nontrivial continuous deformations preserving all dihedral angles and study properties ... More

Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?Jul 26 2017Nov 25 2017We choose some special unit vectors $\boldsymbol{n}_1,\dots,\boldsymbol{n}_5$ in $\mathbb{R}^3$ and denote by $\mathscr{L}\subset\mathbb{R}^5$ the set of all points $(L_1,\dots,L_5)\in\mathbb{R}^5$ with the following property: there exists a compact convex ... More

The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraicAug 17 2015We construct some example of a closed nondegenerate nonflexible polyhedron $P$ in Euclidean 3-space that is the limit of a sequence of nondegenerate flexible polyhedra each of which is combinatorially equivalent to $P$. This implies that the set of flexible ... More

Algebra versus analysis in the theory of flexible polyhedraFeb 02 2009Jul 06 2010Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used ... More

Minkowski-type and Alexandrov-type theorems for polyhedral herissonsNov 19 2002Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex ... More

Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flexJun 27 2019We derive fundamentally new equations that are satisfied by first-order flexes of a flexible polyhedron. Moreover, we indicate two sources of such new equations. These sources are the Dehn invariants and rigidity matrix. The equations derived provide ... More

On Partially Massless Theory in 3 DimensionsOct 10 2014Mar 02 2015We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. ... More

Flexible suspensions with a hexagonal equatorMay 22 2009We construct a flexible (non immersed) suspension with a hexagonal equator in Euclidean 3-space and study its properties related to the Strong Bellows Conjecture which reads as follows: if an immersed polyhedron $\Cal P$ in Euclidean 3-space is obtained ... More

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019Mar 14 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More

Refined open intersection numbers and the Kontsevich-Penner matrix modelFeb 08 2017Feb 16 2017A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J. P. Solomon and the third author, where they introduced open intersection numbers in genus 0. Their construction ... More

From minimal gravity to open intersection theoryApr 15 2019We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with boundaries is defined in terms of boundary cosmological constant $\mu_B$ ... More

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More

Spin and holographic metalsApr 27 2012May 14 2012In this paper we discuss two-dimensional holographic metals from a condensed matter physics perspective. We examine the spin structure of the Green's function of the holographic metal, demonstrating that the excitations of the holographic metal are "chiral", ... More

The effect of intrinsic point defects on ferroelectric polarization behavior of SrTiO$_3$Sep 14 2016The effect of a variety of intrinsic defects and defect clusters in bulk and thin films of SrTiO$_3$ on ferroelectric polarization and switching mechanism is investigated by means of density-functional-theory (DFT) based calculations and the Berry phase ... More

Two-exponential models of gene expression patterns for noisy experimental dataApr 02 2017Motivation: Spatial pattern formation of the primary anterior-posterior morphogenetic gradient of the transcription factor Bicoid (Bcd) has been studied experimentally and computationally for many years. Bcd specifies positional information for the downstream ... More

Classical tau-function for quantum spin chainsDec 14 2011Jul 06 2012For an arbitrary generalized quantum integrable spin chain we introduce a "master T -operator" which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary space. We show ... More

The master T-operator for the Gaudin model and the KP hierarchyJun 05 2013Apr 14 2014Following the approach of [arXiv:1112.3310], we construct the master T -operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also ... More

Simplices with equiareal facesSep 10 2009We study simplices with equiareal faces in the Euclidean 3-space by means of elementary geometry. We present an unexpectedly simple proof of the fact that, if such a simplex is non-degenerate, than every two of its faces are congruent. We show also that ... More

Kondo Breakdown in Topological Kondo InsulatorsJan 13 2015Apr 29 2015Motivated by the observation of light surface states in SmB6, we examine the effects of surface Kondo breakdown in topological Kondo insulators. We present both numerical and analytic results which show that the decoupling of the localized moments at ... More

Spin foam model from canonical quantizationMay 26 2007Feb 22 2008We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found ... More

Reality conditions for Ashtekar gravity from Lorentz-covariant formulationOct 10 2005We show the equivalence of the Lorentz-covariant canonical formulation considered for the Immirzi parameter $\beta=i$ to the selfdual Ashtekar gravity. We also propose to deal with the reality conditions in terms of Dirac brackets derived from the covariant ... More

Enumerative geometry, tau-functions and Heisenberg-Virasoro algebraApr 13 2014May 13 2015In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich-Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the tau-functions in terms of matrix integrals, Virasoro constraints ... More

Matrix Models for Random PartitionsMay 31 2010Mar 17 2011We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation is based on ... More

Hyper-Hermitian quaternionic Kaehler manifoldsMay 25 2001Oct 30 2001We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric hyper-Hermitian quaternionic ... More

The global rigidity of a framework is not an affine-invariant propertyFeb 25 2019Mar 09 2019It is well-known that the property of a bar-and-joint framework `to be infinitesimally rigid' is invariant under projective transformations of Eucliean $d$-space for every $d\geqslant 2$. It is less known that the property of a bar-and-joint framework ... More

Backgrounds of 2D string theory from matrix modelMar 21 2003In the Matrix Quantum Mechanical formulation of 2D string theory it is possible to introduce arbitrary tachyonic perturbations. In the case when the tachyonic momenta form a lattice, the theory is known to be integrable and, therefore, it can be used ... More

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flexSep 02 2018Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows ... More

First-principles computational study of defect clustering in solid solutions of ThO$_{2}$ with trivalent oxidesSep 09 2010The energetics of mixing and defect ordering in solid solutions of fluorite-structured ThO$_{2}$ with oxides of trivalent cations (Sc, In, Y, Nd, La) are investigated by electronic density-functional-theory (DFT). Through DFT calculations of structures ... More

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operatorsNov 22 2011Sep 01 2013In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important feature of this ... More

On weak holonomyMar 27 2004Jul 15 2004We prove that SU(n) (n > 2) and Sp(n)U(1) (n > 1) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group. In both cases ... More

Higher dimensional flexible polyhedraJul 29 1999Sep 02 1999In the previous version of the paper it was announced that ``sphere homeomorphic flexible polyhedra (with self intersections) do really exist in n-dimensional Euclidean, Lobachevskij and spherical spaces for each $n\geq 3$.'' Now the paper has been withdrawn ... More

Prime number logarithmic geometry on the planeApr 12 2002Feb 14 2003We found a regularity of the behavior of primes that allows to represent both prime and natural numbers as infinite matrices with a common formation rule of their rows. This regularity determines a new class of infinite cyclic groups that permit the proposition ... More

On a differential test of homeomorphism, found by N.V. EfimovOct 18 2010In the year 1968 N.V. Efimov has proven the following remarkable theorem: \textit{Let $f:\mathbb R^2\to\mathbb R^2\in C^1$ be such that $\det f'(x)<0$ for all $x\in\mathbb R^2$ and let there exist a function $a=a(x)>0$ and constants $C_1\geqslant 0$, ... More

The first acquaintance with the tensorNov 26 2013The main concepts of the theory of tensors are presented. The emphasis is on the basic notions of tensor algebra and practical skills in culculations involving the Kronecker delta and Levi-Civita symbol. Sixty routine exercises are included. The article ... More

Around the A.D. Alexandrov's theorem on a characterization of a sphereDec 20 2012This is a survey paper on various results relates to the following theorem first proved by A.D. Alexandrov: \textit{Let $S$ be an analytic convex sphere-homeomorphic surface in $\mathbb R^3$ and let $k_1(\boldsymbol{x})\leqslant k_2(\boldsymbol{x})$ be ... More

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flexSep 02 2018Mar 16 2019Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows ... More

How many times can the volume of a convex polyhedron be increased by isometric deformations?Jul 22 2016We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric ... More

Immirzi parameter and fermions with non-minimal couplingFeb 08 2008Jun 16 2008We clarify the role played by the Immirzi parameter in classical gravity coupled to fermions. Considering the general non-minimal coupling, we show that, although the torsion depends explicitly on the Immirzi parameter, in a suitable parametrization the ... More

Matrix Quantum Mechanics and Two-dimensional String Theory in Non-trivial BackgroundsNov 28 2003Dec 04 2003String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string theory which ... More

The new vertices and canonical quantizationApr 13 2010Jun 25 2010We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer ... More

Simplicity and closure constraints in spin foam models of gravityFeb 23 2008Jul 17 2008We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the ... More

Open intersection numbers, matrix models and MKP hierarchyOct 07 2014Mar 11 2015In this paper we conjecture that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a tau-function ... More

Flexible polyhedra in the Minkowski 3-spaceNov 01 2001Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape ... More

Sp(n)U(1)-connections with parallel totally skew-symmetric torsionNov 14 2003Jul 08 2004We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the manifold is locally isomorphic ... More

The first eigenvalue of the Dirac operator on locally reducible Riemannian manifoldsFeb 25 2005We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue ... More

On the total mean curvature of non-rigid surfacesNov 29 2008Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean ... More

New manifestations of the Darboux's rotation and translation fields of a surfaceOct 27 2009We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal bending) and ... More

Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworksJun 19 2000We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient ... More

Hilbert space structure of covariant loop quantum gravityJan 28 2002We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum states are realized ... More

Canonical structure of Tetrad Bimetric GravityAug 29 2013Nov 05 2013We perform the complete canonical analysis of the tetrad formulation of bimetric gravity and confirm that it is ghost-free describing the seven degrees of freedom of a massless and a massive gravitons. In particular, we find explicit expressions for secondary ... More

Twistor Approach to String Compactifications: a ReviewNov 12 2011May 09 2013We review a progress in obtaining the complete non-perturbative effective action of type II string theory compactified on a Calabi-Yau manifold. This problem is equivalent to understanding quantum corrections to the metric on the hypermultiplet moduli ... More

Quantum covariant c-mapFeb 26 2007Mar 23 2008We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler space, which ... More

Test for the Myers-Chern-Simons ActionApr 03 2001Nov 21 2001We present a generalization of the infinitesimal gauge transformation for nonabelian fields on the stack of branes up to the third order in $\Phi$. We test the gauge invariance of the action up to the fifth order in $\Phi$ for $D$-instantons. This substantiates ... More

The Dehn invariants of the Bricard octahedraJan 20 2009We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.

Hermitian spin surfaces with small eigenvalues of the Dolbeault operatorMar 03 2004We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf ... More

An analogue of a van der Waerden's theorem and its application to two-distance preserving mappingsApr 15 2015Apr 17 2015The van der Waerden's theorem reads that an equilateral pentagon in Euclidean 3-space $\Bbb E^3$ with all diagonals of the same length is necessarily planar and its vertex set coincides with the vertex set of some convex regular pentagon. We prove the ... More

An analytical approach to the Rational Simplex ProblemApr 28 2013May 08 2013In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples ... More

The global rigidity of a framework is not an affine-invariant propertyFeb 25 2019It is known that the property of a bar-and-joint framework `to be infinitesimally rigid' is preserved under projective transformations of ambient space. In this article, we prove that the property of a bar-and-joint framework `to be globally rigid' is ... More

Degenerate Plebanski Sector and Spin Foam QuantizationFeb 22 2012May 18 2012We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2) Crane-Yetter ... More

Complex curves and non-perturbative effects in c=1 string theoryDec 21 2004We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation ... More

On the counting of black hole states in loop quantum gravityAug 11 2004We argue that counting black hole states in loop quantum gravity one should take into account only states with the minimal spin at the horizon.

SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameterMay 19 2000Dec 05 2008An so(4,C)-covariant hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so called Immirzi parameter) is developed. It encompasses the Ashtekar-Barbero gravity which serves as a basis of quantum loop ... More

c-map as c=1 stringJan 20 2012We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential. ... More

D-instantons and twistors: some exact resultsFeb 16 2009May 09 2013We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of Type II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping A-cycles) was incorporated ... More

D-branes and complex curves in c=1 string theoryMar 10 2004Jun 30 2004We give a geometric interpretation for D-branes in the c=1 string theory. The geometric description is provided by complex curves which arise in both CFT and matrix model formulations. On the CFT side the complex curve appears from the partition function ... More

(m,n) ZZ branes and the c=1 matrix modelOct 14 2003Jun 30 2004We argue that the origin of non-perturbative corrections exp(-2\pi R n\mu) in the c=1 matrix model is (1,n) D-branes of Zamolodchikovs. We confirm this identification comparing the flow of these corrections under the Sine--Liouville perturbation in the ... More

On choice of connection in loop quantum gravityJul 22 2001Oct 07 2005We investigate the quantum area operator in the loop approach based on the Lorentz covariant hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines which are eigenstates ... More

The effective action and quantum gauge transformationsJul 21 1998Jan 12 1999The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass shell, they can ... More

Sobolev Institute of Mathematics Celebrates its Fiftieth AnniversaryFeb 12 2008This paper describes briefly history and current state of the Sobolev Institute of Mathematics, the biggest research mathematical institute of the Russian Academy of Sciences located east to Ural mountains.

Cut-and-Join operator representation for Kontsevich-Witten tau-functionSep 24 2010Feb 08 2011In this short note we construct a simple cut-and-join operator representation for Kontsevich-Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivation is based on the Virasoro constraints. Possible applications ... More

Givental formula in terms of Virasoro operatorsMay 26 2002Dec 03 2002We present a conjecture that the universal enveloping algebra of differential operators $\frac{\p}{\p t_k}$ over $\mathbb{C}$ coincides in the origin with the universal enveloping algebra of the (Borel subalgebra of) Virasoro generators from the Kontsevich ... More

On the number of solutions of a quadratic equation in a normed spaceJun 08 2015We study an equation $Qu=g$, where $Q$ is a continuous quadratic operator acting from one normed space to another normed space. Obviously, if $u$ is a solution of such equation then $-u$ is also a solution. We find conditions implying that there are no ... More

A sufficient condition for a polyhedron to be rigidDec 16 2018Dec 26 2018We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing ... More

How many times can the volume of a convex polyhedron be increased by isometric deformations?Jul 22 2016Mar 01 2017We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric ... More

TBA for non-perturbative moduli spacesMar 21 2010Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton ... More

c=1 from c<1: Bulk and boundary correlatorsApr 25 2005Sep 29 2005We study the c_L=25 limit, which corresponds to c=1 string theory, of bulk and boundary correlation functions of Liouville theory with FZZT boundary conditions. This limit is singular and requires a renormalization of vertex operators. We formulate a ... More

Area spectrum in Lorentz covariant loop gravityMar 28 2001May 03 2001We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of non-commutative ... More

Heat kernel for non-minimal operators on a Kahler manifoldJan 17 1996The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the Seeley coefficients ... More

Dynamic systems with quantum behaviourJan 26 2009Apr 08 2009It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions corresponding to quantum ... More

Symmetry Properties of Electromagnetic Field in the MatterFeb 01 2009Feb 16 2009The sets ${\Phi({F}^{\mu \nu})}, {\Phi(\tilde {F}^{\mu \nu})}$ of linear functionals on the space $< F,+,\cdot >$ represent themself linear space $< \Phi,+,\cdot >$ over the field of \textit{scalars} $P$, which is dual to space $< F,+,\cdot >$, but it ... More

Reply to the comment by C. Capan and K. Behnia on "Nernst effect in poor conductors and in the cuprate superconductors" (cond-mat/0501288)Aug 19 2005The comment criticisms (cond-mat/0501288) are completely out of line with the context of the commented theory (Phys. Rev. Lett. v.93, 217002 (2004)). The comment neglected essential parts of the theory, which actually addressed all relevant experimental ... More

Theory of tunnelling into and from cupratesApr 28 1998A single-particle spectral density is proposed for cuprates taking into account the bipolaron formation, realistic band structure, thermal fluctuations and disorder. Tunnelling and photoemission (PES) spectra are described, including the temperature independent ... More

Normal state Nernst effect, semiconducting-like resistivity and diamagnetism of underdoped cupratesJul 12 2005Dec 28 2005Semiconducting-like low-temperature in-plane resistivity indicates that there are no remnants of superconductivity above the resistive phase transition at T > Tc in underdoped cuprates. The model with the chemical potential pinned near the mobility edge ... More

Superlight bipolarons and a checkerboard d-wave condensate in cupratesJun 25 2003Jun 26 2003The seminal work by Bardeen, Cooper and Schrieffer taken further by Eliashberg to the intermediate coupling solved the problem of conventional superconductors about half a century ago. The Froehlich and Jahn-Teller electron-phonon interactions were identified ... More

d-Wave bipolaronic stripes and two energy scales in cupratesOct 04 2000Oct 05 2000There is strong experimental evidence for pairing of polaronic carriers in the normal state, two distinct energy scales, d-wave superconducting order parameter,and charge segregation in the form of stripes in several cuprates.All these remarkable phenomena ... More

Hypermultiplet metric and D-instantonsDec 28 2014Jan 08 2015We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way ... More

Modularity, Quaternion-Kahler spaces and Mirror SymmetryJun 07 2013Feb 13 2014We provide an explicit twistorial construction of quaternion-Kahler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z). The deformation is not assumed to preserve any continuous isometry and ... More

Theta series, wall-crossing and quantum dilogarithm identitiesNov 09 2015Jul 26 2016Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau ... More

Bi-gravity with a single gravitonApr 26 2019We analyze a bi-gravity model based on the first order formalism, having as fundamental variables two tetrads but only one Lorentz connection. We show that on a large class of backgrounds its linearization agrees with general relativity. At the non-linear ... More

Deformations of nearly parallel G_2-structuresJan 11 2011We study the infinitesimal deformations of a proper nearly parallel G_2-structure and prove that they are characterized by a certain first order differential equation. In particular we show that the space of infinitesimal deformations modulo the group ... More

Bipolaronic proximity and other unconventional effects in cuprate superconductorsJan 24 2008Feb 04 2008There is compelling evidence for a strong electron-phonon interaction (EPI) in cuprate superconductors from the isotope effects on the supercarrier mass, high resolution angle resolved photoemission spectroscopies (ARPES), a number of optical and neutron-scattering ... More

Unconventional superconducting pairing by conventional phononsMay 18 2007May 29 2007The common wisdom that the phonon mechanism of electron pairing in the weak-coupling Bardeen-Cooper-Schrieffer (BCS) superconductors leads to conventional s-wave Cooper pairs is revised. An inevitable anisotropy of sound velocity in crystals makes the ... More

Strong-coupling superconductivity beyond BCS and the key pairing interaction in cuprate superconductorsDec 23 2010Dec 24 2010It has been now over 20 years since the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 and yet, despite intensive effort, no universally accepted theory exists about the origin of high-temperature superconductivity. ... More

Strong-Coupling Theory of High Temperature SuperconductivityAug 31 2005Dec 28 2005High-temperature superconductivity (HTS) of cuprates represents a challenge to the conventional theory. Here I review a multi-polaron approach to the problem based on our extension of the BCS theory to the strong-coupling regime. Since there is almost ... More