138 citations · 1.8k across the 53 of their papers we have counts for
37 papers · 1 filter
Correlators in the theory of Integral Discriminants
A. Morozov, Sh. Shakirov
Integral discriminants provide a simple and fundamental model for non-Gaussian integrals, associated with homogeneous polynomials of degree r in n variables. We argue that, in this…
5D AGT conjecture for circular quivers
A. Mironov, A. Morozov, Sh. Shakirov
The best way to represent generic conformal blocks is provided by the free-field formalism, where they acquire a form of multiple Dotsenko-Fateev-like integrals of the screening op…
Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
A. Mironov, A. Morozov, A. Popolitov +1
We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables . One can look at it as a mixture of the Gaussian and logarithmic (Selberg) p…
Summing up perturbation series around superintegrable point
A. Mironov, A. Morozov, A. Popolitov +1
We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on…
Double Inozemtsev Limits of the Quantum DELL System
Alexander Gorsky, Peter Koroteev, Olesya Koroteeva +1
In this letter we study various Inozemtsev-type limits of the quantum double elliptic (DELL) system when both elliptic parameters are sent to zero at different rates, while the cou…
Harer-Zagier formulas for knot matrix models
Alexei Morozov, Aleksandr Popolitov, Shamil Shakirov
Knot matrix models are defined so that the averages of characters are equal to knot polynomials. From this definition one can extract single trace averages and generation functions…
Quantization of Harer-Zagier formulas
Alexei Morozov, Aleksandr Popolitov, Shamil Shakirov
We derive the analogues of the Harer-Zagier formulas for single- and double-trace correlators in the q-deformed Hermitian Gaussian matrix model. This fully describes single-trace c…
The Quantum DELL System
Peter Koroteev, Shamil Shakirov
We propose quantum Hamiltonians of the double elliptic many-body integrable system (DELL) and study its spectrum. These Hamiltonians are certain elliptic functions of coordinates a…
Solving q-Virasoro constraints
Rebecca Lodin, Aleksandr Popolitov, Shamil Shakirov +1
We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators un…
Refined Topological Branes
Can Kozçaz, Shamil Shakirov, Cumrun Vafa +1
We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary condition…
On (q,t)-deformation of Gaussian matrix model
A. Morozov, A. Popolitov, Sh. Shakirov
The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian measures. Then substi…
Argyres-Douglas Theories, Modularity of Minimal Models and Refined Chern-Simons
Can Kozçaz, Shamil Shakirov, Wenbin Yan
The Coulomb branch indices of Argyres-Douglas theories on are recently identified with matrix elements of modular transforms of certain vertex operator al…
On the block structure of the quantum R-matrix in the three-strand braids
L. Bishler, An. Morozov, A. Sleptsov +1
Quantum -matrices are the building blocks for the colored HOMFLY polynomials. In the case of three-strand braids with an identical finite-dimensional irreducible repre…
Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
Clay Cordova, Ben Heidenreich, Alexandr Popolitov +1
We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well a…
Quantum Racah matrices and 3-strand braids in representation [3,3]
Sh. Shakirov, A. Sleptsov
This paper is a next step in the project of systematic description of colored knot polynomials started in arXiv:1506.00339. In this paper, we managed to explicitly find the $\texti…
Refined Chern-Simons Theory in Genus Two
Semeon Arthamonov, Shamil Shakirov
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The…
Gauge/Vortex duality and AGT
Mina Aganagic, Shamil Shakirov
This is the 12th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories" ed. J. Teschner. This article describes one way to understand an importan…
-Triality
Mina Aganagic, Nathan Haouzi, Shamil Shakirov
A_n-type AGT correspondence anticipates that conformal blocks of A_n Toda CFT are related to partition functions of a family of 4d N=2 SCFTs. We use gauge/vortex duality to both gi…
Gauge/Liouville Triality
Mina Aganagic, Nathan Haouzi, Can Kozcaz +1
Conformal blocks of Liouville theory have a Coulomb-gas representation as Dotsenko-Fateev (DF) integrals over the positions of screening charges. For q-deformed Liouville, the conf…
Refined Chern-Simons Theory and Topological String
Mina Aganagic, Shamil Shakirov
We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes. We derive the refined topological vertex o…
Torus HOMFLY as the Hall-Littlewood Polynomials
A. Mironov, A. Morozov, Sh. Shakirov
We show that the HOMFLY polynomials for torus knots T[m,n] in all fundamental representations are equal to the Hall-Littlewood polynomials in representation which depends on m, and…
Interplay between MacDonald and Hall-Littlewood expansions of extended torus superpolynomials
A. Mironov, A. Morozov, Sh. Shakirov +1
In arXiv:1106.4305 extended superpolynomials were introduced for the torus links T[m,mk+r], which are functions on the entire space of time variables and, at expense of reducing th…
Refined Chern-Simons Theory and Knot Homology
Mina Aganagic, Shamil Shakirov
The refined Chern-Simons theory is a one-parameter deformation of the ordinary Chern-Simons theory on Seifert manifolds. It is defined via an index of the theory on N M5 branes, wh…
Proving AGT conjecture as HS duality: extension to five dimensions
A. Mironov, A. Morozov, Sh. Shakirov +1
We extend the proof from arXiv:1012.3137, which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an addition…