# Yegor Zenkevich

## Contact Details

NameYegor Zenkevich |
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## Pub CategoriesHigh Energy Physics - Theory (8) Mathematics - Mathematical Physics (6) Mathematical Physics (6) Mathematics - Representation Theory (2) Mathematics - Quantum Algebra (2) General Relativity and Quantum Cosmology (1) |

## Publications Authored By Yegor Zenkevich

We derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki (DIM) algebra U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1). We demonstrate that certain refined topological string amplitudes satisfy these equations and find that the braiding transformations are performed by the R-matrix of U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1). The resulting syste is the uplifting of the \widehat{\mathfrak{u}}_1 Wess-Zumino-Witten model. Read More

We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2,R) symmetry. Read More

We find new universal factorization identities for generalized Macdonald polynomials on the topological locus. We prove the identities (which include all previously known forumlas of this kind) using factorization identities for matrix model averages, which are themselves consequences of Ding-Iohara-Miki constraints. Factorized expressions for generalized Macdonald polynomials are identified with refined topological string amplitudes containing a toric brane on an intermediate preferred leg, surface operators in gauge theory and certain degenerate CFT vertex operators. Read More

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the Yangian case by A.~Smirnov but less general. Read More

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity. Read More

We derive quantum spectral curve equation for (q,t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory. Read More

We study five dimensional AGT correspondence by means of the q-deformed beta-ensemble technique. We provide a special basis of states in the q-deformed CFT Hilbert space consisting of generalized Macdonald polynomials, derive the loop equations for the beta-ensemble and obtain the factorization formulas for the corresponding matrix elements. We prove the spectral duality for Nekrasov functions and discuss its meaning for conformal blocks. Read More

Nekrasov functions were conjectured in \cite{Mironov:2009uv} to be related to exact Bohr-Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for the case of the pure $SU(N_c)$ gauge theory in \cite{Mironov:2009dv} and \cite{Popolitov:2010bz}. Here we successfully perform a set of checks in the case of gauge group $SU(N_c)$ with additional $N_f$ fundamental hypermultiplets. Read More