Related papers: On the Virasoro constraints for torus knots
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in $E$-theory. The other type is by module multiplications in $K$-theory, which also yields an…
Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus…
$R$-coloured knot polynomials for $m$-strand torus knots $Torus_{[m,n]}$ are described by the Rosso-Jones formula, which is an example of evolution in $n$ with Lyapunov exponents, labelled by Young diagrams from $R^{\otimes m}$. This means…
In this paper we propose a quantum gauge system from which we construct generalized Wilson loops which will be as quantum knots. From quantum knots we give a classification table of knots where knots are one-to-one assigned with an integer…
We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk…
The Wess-Zumino consistency conditions for Lorentz and diffeomorphism anomalies are discussed by introducing an operator 'delta' which allows to decompose the exterior derivative as a BRS commutator.
An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra $U_q(\hat{sl}_2)$. A similar construction is proposed for the elliptic algebra…
We investigate in details how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a…
We investigate the supereigenvalue model in the Ramond sector. We prove that its partition function can be obtained by acting on elementary functions with exponents of the given operators. The Virasoro constraints for this supereigenvalue…
We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial.…
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…
This thesis is divided into two parts, where in the first part we investigate the computation of Virasoro 1-point blocks on the torus in the framework of Zamolodchikov's recursion relation. It is widely accepted that this recursion relation…
The book is devoted to the formation and dynamics of localized structures (vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and…
In this paper, we prove formulas for the action of Virasoro operators on Hall-Littlewood polynomials at roots of unity.
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schr\"odinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on…
We compute rho-invariant for iterated torus knots $K$ for the standard representation of the knot group given by abelianisation. For algebraic knots, this invariant turns out to be very closely related to an invariant of a plane curve…
We show that the torus knot topology is inherent in electromagnetic and gravitational radiation by constructing spin-$N$ fields based on this topology from the elementary states of twistor theory. The twistor functions corresponding to the…
We consider processes which produce final state hadrons whose energy is much greater than their mass. In this limit interactions involving collinear fermions and gluons are constrained by a symmetry, and we give a general set of rules for…