A5075669127- Algebraic structures and combinatorial models
- Black Holes and Theoretical Physics
- Nonlinear Waves and Solitons
- Geometric and Algebraic Topology
- Homotopy and Cohomology in Algebraic Topology
- Advanced Algebra and Geometry
- Advanced Combinatorial Mathematics
- Advanced Topics in Algebra
- Quantum Chromodynamics and Particle Interactions
- Cosmology and Gravitation Theories
- Noncommutative and Quantum Gravity Theories
- Particle physics theoretical and experimental studies
- Molecular spectroscopy and chirality
- Quantum Mechanics and Non-Hermitian Physics
- Quantum chaos and dynamical systems
- advanced mathematical theories
- Matrix Theory and Algorithms
- Advanced Operator Algebra Research
- Algebraic Geometry and Number Theory
- Geometry and complex manifolds
- Connective tissue disorders research
- Theoretical and Computational Physics
- Mathematical functions and polynomials
- Mathematical Dynamics and Fractals
- Random Matrices and Applications
Institute for Information Transmission Problems
2015-2024
Kurchatov Institute
2018-2024
Moscow Institute of Physics and Technology
2009-2024
Institute for Theoretical and Experimental Physics
2014-2023
Lomonosov Moscow State University
2008-2022
Saint Petersburg Mining University
2022
Sergeev Institute of Environmental Geoscience
2022
Moscow Power Engineering Institute
2020
Moscow Aviation Institute
2020
National Research Nuclear University MEPhI
2014-2018
The free field representation or "bosonization" rule 1 for Wess-Zumino-Witten model (WZWM) with arbitrary Kac-Moody algebra and central charge is discussed. Energy-momentum tensor, arising from Sugawara construction, quadratic in the fields. In this way, all known formulae conformal blocks correlators may be easily reproduced as certain linear combinations of these Generalization to on Riemann surfaces straightforward. However, projection rules spirit Ref. 2 are not specified. special role...
In arXiv:0910.5670 we suggested that the Nekrasov function with one non-vanishing deformation parameter \epsilon is obtained by standard Seiberg-Witten contour-integral construction. The only difference differential pdx substituted its quantized version for corresponding integrable system, and contour integrals become exact monodromies of wave function. This provides an explicit formulation earlier guess in arXiv:0908.4052. this paper successfully check suggestion first order \epsilon^2...
Ward identities in the most general "network matrix model" from [1] can be described terms of Ding–Iohara–Miki algebras (DIM). This confirms an expectation that such and their various limits/reductions are relevant substitutes/deformations Virasoro/W-algebra for (q,t) (q1,q2,q3) deformed network models. Exhaustive these purposes should Pagoda triple-affine elliptic DIM, which corresponds to networks associated with 6d gauge theories adjoint matter (double systems). We provide some details on...
Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple what we call balanced networks. Then, Ward identities (known under names of Virasoro/ $$ \mathcal{W} -constraints or loop equations regularity condition qq-characters) also promoted to DIM level, where they become corollaries a single identity.
We extend the old formalism of cut-and-join operators in theory Hurwitz $\tau$-functions to description a wide family KP-integrable {\it skew} $\tau$-functions, which include, particular, newly discovered interpolating WLZZ models. Recently, simplest them was related superintegrable two-matrix model with two potentials and one external matrix field. Now we provide detailed proofs, generalization multi-matrix representation, propose $\beta$ deformation as well. The general is generated by...
Even though matrix model partition functions do not exhaust the entire set of tau-functions relevant for string theory, they seem to be elementary building blocks many others and properly capture fundamental symplicial nature quantum gravity theory. We propose consider as new special functions. This means should investigated put into some standard form, with no reference particular applications. At same time, tables lists properties full enough avoid discoveries unexpected peculiarities in...
The Kazakov-Migdal model, if considered as a functional of external fields, can always be represented an expansion over characters the GL group. integration “matter fields” interpreted going model (the space all highest weight representations) GL. In case compact unitary groups integrals should substituted by discrete sums lattice. D=0 version is generalized Kontsevich integral, which in above-mentioned (discrete) situation coincides with partition function 2D Yang-Mills theory target genus...
As anticipated in Ref. 1, elaborated Refs. 2–4, and explicitly formulated 5, the Dotsenko–Fateev integral discriminant coincides with conformal blocks, thus providing an elegant approach to AGT conjecture, without any reference auxiliary subject of Nekrasov functions. Internal dimensions blocks this identification are associated choice contours: parameters Dijkgraaf–Vafa phase corresponding matrix models. In paper, we provide further evidence support identity for 6-parametric family 4-point...