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Search: authors:"Yegor Zenkevich"

4 papers found.
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Exact solutions and critical chaos in dilaton gravity with a boundary

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. After introducing general ...

Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions

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 SU(2) ...

Toric Calabi-Yau threefolds as quantum integrable systems. \( \mathrm{\mathcal{R}} \) -matrix and \( \mathrm{\mathcal{R}}\mathcal{T}\mathcal{T} \) relations

\( \mathrm{\mathcal{R}} \)-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than the one through the universal \( \mathrm{\mathcal{R}} \)-matrix used for a similar calculation in the Yangian case by A. Smirnov but less general. We investigate the interplay between the \( ...

Explicit examples of DIM constraints for network matrix models

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/\( \mathcal{W} \)-constraints or ...