Related papers: On the Virasoro constraints for torus knots
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the…
We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S^3. The key role is played by the SL(2,Z) transformation, which generates a general torus knot from the unknot. Applying…
In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group, as well as different definitions of contiguous and suitably connected. We…
In 2003, Hikami and Kirillov uncovered an intriguing connection between torus knots $\mathcal{K}_{(P,Q)}$ and Virasoro minimal models $\mathcal{M}(P,Q)$ by relating the Kashaev invariants of the knots to the characters of the corresponding…
The classical Volterra model, equipped with the Faddeev-Takhtadjan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so called…
This is the second paper in a series on {\it Virasoro constraints for Cohomological Field Theory}. We derive the ancestor Virasoro constraints for the topological recursion (TR) for an arbitrary spectral curve and establish the descendent…
We construct $W_3$ null vectors of a restricted class explicitly in two different forms. The method we use is an extension of that of Bauer et al.~in the Virasoro case. Our results are analogous to the formulae of Benoit and St.~Aubin for…
We describe graded contractions of Virasoro algebra. The highest weight representations of Virasoro algebra are constructed. The reducibility of representations is analysed. In contrast to standart representations the contracted ones are…
Aspects of black hole thermodynamics and information loss can be derived as a consequence of Virasoro symmetry. To bolster the connection between Virasoro conformal blocks and AdS$_3$ quantum gravity, we study sl$(2)$ Chern-Simons Wilson…
We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for…
In this paper, we study certain Virasoro frames for lattice vertex operator algebras and their $\Z_2$-orbifolds using linear codes over $\Z_4$. We also compute the corresponding frame stabilizer from the view point of binary codes and…
We consider sl(2) minimal conformal field theories and the dual parafermion models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS) models and its Virasoro modules expressed in terms of paths, we propose a general…
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [arXiv:0812.4776]. We find the algebraic construction to be related to a particular…
We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two…
We investigate the algebra generated by the topological Wilson loop operators in WZW models. Wilson loops describe the nontrivial fixed points of the boundary renormalization group flows triggered by Kondo perturbations. Their enveloping…
We prove that all the correlation functions in the $(1,q)$ models are calculable using only the Virasoro and the $W^{(3)}$ constraints. This result is based on the invariance of correlators with respect to an interchange of the order of the…
It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is…
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…
The paragrassmann calculus proposed earlier is applied to constructing paraconformal transformations and paragrassmann generalizations of the Virasoro-Neveu-Schwarz-Ramond algebras.
We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.