arXiv subjects

Yegor Zenkevich

Publications and source records attributed to Yegor Zenkevich.

At least 19 recordsLinked to original sources

arXiv2026

Wall crossing, string networks and quantum toroidal algebras

We investigate BPS states in 4d N=4 supersymmetric Yang-Mills theory and the corresponding (p, q) string networks in Type IIB string theory. We propose a new interpretation of the algebra of line operators in this theory as a tensor product of vector representations of a quantum toroidal algebra, which determines protected spin characters of all framed BPS states. We identify the SL(2,Z)-noninvariant choice of the coproduct in the quantum toroidal algebra with the choice of supersymmetry subalgebra preserved by the BPS states and interpret wall crossing operators as Drinfeld twists of the coproduct. Kontsevich-Soibelman spectrum generator is then identified with Khoroshkin-Tolstoy universal R-matrix.

hep-th↗

arXiv2026

Spiralling branes and R-matrices

We extend the dictionary between Type IIB branes and representations of the Ding-Iohara-Miki (DIM) algebra to the case when one of the space directions is a circle. It is well-known that the worldvolume theory on branes wrapping the circle is a 5d $\mathcal{N}=1$ gauge theory with adjoint matter, or more generally of cyclic quiver type, and the corresponding intertwiners of the DIM algebra give their Nekrasov partition functions. However, we find that there exists a much wider natural class of intertwiners corresponding to branes spiralling around the compactified direction, with many interesting properties. We consider two examples, one corresponding to a spiralling D5 brane and another to a D3 brane. The former gives rise to the K-theoretic vertex function counting sheaves on $\mathbb{C}^3$ while the latter produces the "non-stationary elliptic Ruijsenaars wavefunctions" introduced recently by Shiraishi.

hep-th↗

arXiv2024

Spiralling branes, affine qq-characters and elliptic integrable systems

We apply the spiralling branes technique introduced in arXiv:2312.16990 to many-body integrable systems. We start by giving a new R-matrix description of the trigonometric Ruijsenaars-Schneider (RS) Hamiltonians and eigenfunctions using the intertwiners of quantum toroidal algebra. We then consider elliptic deformations of the RS system, elucidate how Shiraishi functions appear naturally in the process and relate them to certain special infinite system of intertwiners of the algebra. We further show that there are two distinguished elliptic deformations, one of which leads to the conventional elliptic RS Hamiltonians, while the other produces trigonometric Koroteev-Shakirov Hamiltonians. Along the way we prove the fully noncommutative version of the "noncommutative Jacobi identities" for affine qq-characters recently introduced by Grekov and Nekrasov.

hep-th↗

arXiv2023

On R-matrix formulation of qq-characters

We introduce an R-matrix formulation of qq-characters and corresponding Frenkel-Reshetikhin deformed W-algebras. The R-matrix featuring in the construction is of Ding-Iohara-Miki (DIM) algebra, while the type of the qq-character is determined by the network of Fock representations corresponding to a web of 5-branes geometrically engineering a quiver gauge theory. Our formulation gives a unified description of qq-characters of $A_n$ type and their elliptic uplifts.

hep-th↗

arXiv2022

Hanany-Witten brane crossing and Ding-Iohara-Miki algebra

We further develop the correspondence between representations of Ding-Iohara-Miki (DIM) algebra and Type IIB branes. In particular we explicitly compute the Hanany-Witten type 5-brane crossing operator which plays the role of the $R$-matrix and has interesting combinatorial properties. We explore the corresponding lattice integrable models and notice a possible connection with statistics of plane partitions.

hep-th↗

arXiv2021

On pentagon identity in Ding-Iohara-Miki algebra

We notice that the famous pentagon identity for quantum dilogarithm functions and the five-term relation for certain operators related to Macdonald polynomials discovered by Garsia and Mellit can both be understood as specific cases of a general "master pentagon identity" for group-like elements in the Ding-Iohara-Miki (or quantum toroidal, or elliptic Hall) algebra. We perform some checks of this remarkable identity and discuss its implications.

math.QA↗

arXiv2021

Solution of tetrahedron equation and cluster algebras

We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations. As an application of the new formalism we show how to construct integrable system with spectral curve with arbitrary symmetric Newton polygon. Finally, we embed this integrable system into double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to general non-symmetric Newton polygons, and prove Lemma, which classifies conjugacy classes in double affine Weyl groups of $A$-type by Newton polygons.

nlin.SI↗

arXiv2021

Higgsed network calculus

We introduce a formalism for describing holomorphic blocks of 3d quiver gauge theories using networks of Ding-Iohara-Miki algebra intertwiners. Our approach is very direct and gives an explicit identification of the blocks with Dotsenko-Fateev type integrals for q-deformed quiver W-algebras. We also explain how quiver theories corresponding to Dynkin diagrams of superalgebras arise, write down the corresponding partition functions and W-algebras, and explain the connection with supersymmetric Macdonald-Ruijsenaars commuting Hamiltonians.

hep-th↗

arXiv2020

Mixed network calculus

We show how to combine higgsed topological vertices introduced in our previous work with conventional refined topological vertices. We demonstrate that the extended formalism describes very general interacting D5-NS5-D3 brane systems. In particular, we introduce new types of intertwining operators of Ding-Iohara-Miki algebra between different types of Fock representations corresponding to the crossings of NS5 and D5 branes. As a byproduct we obtain an algebraic description of the Hanany-Witten brane creation effect, give an efficient recipe to compute the brane factors in 3d N=2 and N=4 quiver gauge theories and demonstrate how 3d S-duality appears in our setup.

hep-th↗

arXiv2020

4d higgsed network calculus and elliptic DIM algebra

Supersymmetric gauge theories of certain class possess a large hidden nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which can be used to compute their partition functions and correlators very efficiently. We lift the DIM-algebraic approach developed to study holomorphic blocks of 3d linear quiver gauge theories one dimension higher. We employ an algebraic construction in which the underlying trigonometric DIM algebra is elliptically deformed, and an alternative geometric approach motivated by topological string theory. We demonstrate the equivalence of these two methods, and motivated by this, prove that elliptic DIM algebra is isomorphic to the direct sum of a trigonometric DIM algebra and an additional Heisenberg algebra.

hep-th↗

arXiv2020

ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds

We study the moduli space of $SU(4)$ invariant BPS conditions in supersymmetric gauge theory on non-commutative ${\mathbb C}^4$ by means of an ADHM-like quiver construction and we classify the invariant solutions under the natural toric action in terms of solid partitions. In the orbifold case ${\mathbb C}^4/G$, $G$ being a finite subgroup of $SU(4)$, the classification is given in terms of coloured solid partitions. The statistical weight for their counting is defined through the associated equivariant cohomological gauge theory. We explicitly compute its partition function on ${\mathbb C}^4$ and ${\mathbb C}^2\times\left({\mathbb C}^2/{\mathbb Z}_2\right)$ which conjecturally provides the corresponding orbifold Donaldson-Thomas invariants.

hep-th↗

arXiv2020

Dilaton gravity with a boundary: from unitarity to black hole evaporation

We point out that two-dimensional Russo-Susskind-Thorlacius (RST) model for evaporating black holes is locally equivalent - at the full quantum level - to flat-space Jackiw-Teitelboim (JT) gravity that was recently shown to be unitary. Globally, the two models differ by a reflective spacetime boundary added in the RST model. Treating the boundary as a local and covariant deformation of quantum JT theory, we develop sensible semiclassical description of evaporating RST black holes. Nevertheless, our semiclassical solutions fail to resolve the information recovery problem, and they do not indicate formation of remnants. This means that either the standard semiclassical method incorrectly describes the evaporation process or the RST boundary makes the flat-space JT model fundamentally inconsistent.

hep-th↗

arXiv2020

Quiver $\text{W}_{ε_1,ε_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories

We construct an $ε$-deformation of W algebras, corresponding to the additive version of quiver $\text{W}_{q,t^{-1}}$ algebras which feature prominently in the 5d version of the BPS/CFT correspondence and refined topological strings on toric Calabi-Yau's. This new type of algebras fill in the missing intermediate level between $q$-deformed and ordinary W algebras. We show that $ε$-deformed W algebras are spectral duals of conventional W algebras, in particular the $ε$-deformed conformal blocks manifestly reproduce instanton partition functions of 4d $\mathcal{N}=2$ quiver gauge theories in the full $Ω$-background and give dual integral representations of ordinary W conformal blocks.

hep-th↗

arXiv2019

$\mathfrak{gl}_N$ Higgsed networks

We generalize the framework of Higgsed networks of intertwiners to the quantum toroidal algebra associated to Lie algebra $\mathfrak{gl}_N$. Using our formalism we obtain a systems of screening operators corresponding to W-algebras associated to toric strip geometries and reproduce partition functions of 3d theories on orbifolded backgrounds.

hep-th↗

arXiv2018

T[U(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

We study various duality webs involving the 3d FT[SU(N)] theory, a close relative of the T[SU(N)] quiver tail. We first map the partition functions of FT[SU(N)] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks. Then we show how to obtain the FT[SU(N)] partition function by Higgsing a 5d linear quiver gauge theory, or equivalently from the refined topological string partition function on a certain toric Calabi-Yau three-fold. 3d spectral duality in this context descends from 5d spectral duality. Finally we discuss the 2d reduction of the 3d spectral dual pair and study the corresponding limits on the q-Toda side. In particular we obtain a new direct map between the partition function of the 2d FT[SU(N)] GLSM and an (N+2)-point Toda conformal block.

hep-th↗

arXiv2018

Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles

We consider T[SU(N)] and its mirror, and we argue that there are two more dual frames, which are obtained by adding flipping fields for the moment maps on the Higgs and Coulomb branch. Turning on a monopole deformation in T[SU(N)], and following its effect on each dual frame, we obtain four new daughter theories dual to each other. We are then able to construct pairs of 3d spectral dual theories by performing simple operations on the four dual frames of T[SU(N)]. Engineering these 3d spectral pairs as codimension-two defect theories coupled to a trivial 5d theory, via Higgsing, we show that our 3d spectral dual theories descends from the 5d spectral duality, or fiber base duality in topological string. We provide further consistency checks about the web of dualities we constructed by matching partition functions on the three sphere, and in the case of spectral duality, matching exactly topological string computations with holomorphic blocks.

hep-th↗

arXiv2018

3d field theory, plane partitions and triple Macdonald polynomials

We argue that MacMahon representation of Ding-Iohara-Miki (DIM) algebra spanned by plane partitions is closely related to the Hilbert space of a 3d field theory. Using affine matrix model we propose a generalization of Bethe equations associated to DIM algebra with solutions also labelled by plane partitions. In a certain limit we identify the eigenstates of the Bethe system as new triple Macdonald polynomials depending on an infinite number of families of time variables. We interpret these results as first hints of the existence of an integrable 3d field theory, in which DIM algebra plays the same role as affine algebras in 2d WZNW models.

hep-th↗

arXiv2017

Quantum spectral curve for (q,t)-matrix model

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.

hep-th↗