arXiv subjects

Andrei Mironov

Publications and source records attributed to Andrei Mironov.

16 recordsLinked to original sources

arXiv2026

NTIRE 2026 Low-light Enhancement: Twilight Cowboy Challenge

This paper presents a review of the NTIRE 2026 Low-light Enhancement: Twilight Cowboy Challenge. The objective of the competition was to merge a set of misaligned smartphone images in the raw domain, captured in low-light conditions, into a single, clean image. Introduced setup simultaneously addresses two problems of low-light photography: visual degradations such as high noise and mixed scene illuminants, and the geometric inconsistencies caused by hand movement during multi-frame capture. To advance research in low-light and nighttime computational photography, a challenging dataset was collected comprising 585 real-world scenes, spanning indoor low-light and outdoor nighttime conditions, for training and benchmarking participant solutions. The competition employed a three-stage evaluation protocol: automatic validation via the CodaBench platform in stages one and two, followed by blind assessment on a private test set for the final ranking. Ten teams surpassed the established baseline, achieving improvements of up to +6.49 dB in PSNR and +0.0101 in SSIM, thereby establishing new state-of-the-art performance for burst-based low-light image enhancement. These results demonstrate significant progress in handling real-world noise, motion, and illumination variability in the low-light setting. Comprehensive results, leaderboards, and additional information are publicly available at https://nightimaging.org.

cs.CV↗

arXiv2026

Torus Knots in Adjoint Representation

We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.

hep-th↗

arXiv2026

A note on universality in refined Chern-Simons theory

We discuss various forms of refinements of Vogel's universality in Chern-Simons theory. While the original universality applies to arbitrary simple Lie groups, its counterpart in refined Chyrn-Simons theory is restricted to simply laced Lie groups.

hep-th↗

arXiv2025

Panhandle polynomials of torus links and geometric applications

We use a decomposition of the tensor of the fundamental representation of the quantum group $U_q(\mathfrak{sl}_N)$ and the Rosso-Jones formula to establish a peculiar ``panhandle'' shape of the HOMFLY-PT polynomial of the reverse parallel of torus knots and links. Due to their panhandle-like intrinsic properties, the HOMFLY-PT polynomial is referred to as a ``panhandle polynomial''. With the help of the $\ell$-invariant, this extends to links the Etnyre-Honda result about the arc index and maximal Thurston-Bennequin invariant of torus knots. It has further geometric consequences, related to the braid index, the existence of minimal string Bennequin surfaces for banded and Whitehead doubled links, the Bennequin sharpness problem, and the equivalence of their quasipositivity and strong quasipositivity. We extend these properties to torus links, which relate to the classification of their component-wise Thurston-Bennequin invariants. Finally, we discuss the definition of the $\ell$-invariant for general links.

math.GT↗

arXiv2025

Tau functions of the UC hierarchy as partition functions of matrix models

We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to multi-matrix models case, which corresponds to the multi-component UC hierarchy.

hep-th↗

arXiv2025

Macdonald deformation of Vogel's universality and link hyperpolynomials

Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $α,β,γ$, which are homogeneous coordinates of Vogel's plane. Actually this is true (if at all) only for a piece of representation theory captured by knot/Chern-Simons theory, where some irreducible representations are often undistinguishable and combined into new ``universally-irreducible" entities (uirreps). We consider from this point of view the recently discovered Macdonald deformation of quantum dimensions, for which a kind of universality holds for the ADE series. The claim is that universal are not Macdonald dimensions themselves, but their products with Littlewood-Richardson coefficients, which themselves are functions of $q$ and $t$ in Macdonald theory. These products are precisely what arises in knot/refined Chern-Simons theory. Actually, we consider the simplest decomposition of adjoint square into six uirreps and obtain the universal formulas for hyperpolynomials of the Hopf link and, more generally, of the torus links $T[2,2n]$.

hep-th↗

arXiv2025

Torus knots in adjoint representation and Vogel's universality

Vogel's universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $α,β,γ$, which are homogeneous coordinates of Vogel's plane. It is associated with representation theory within the framework of Chern-Simons theory only, and gives rise to universal knot invariants. We extend the list of these latter further, and explain how to deal with the adjoint invariants for the torus knots $T[m,n]$ considering the case of $T[4,n]$ with odd $n$ in detail.

hep-th↗

arXiv2025

On Refined Vogel's universality

In accordance with P. Vogel, a set of algebra structures in Chern-Simons theory can be made universal, independent of a particular family of simple Lie algebras. In particular, this means that various quantities in the adjoint representations of these simple Lie algebras such as dimensions and quantum dimensions, Racah coefficients, etc. are simple rational functions of two parameters on Vogel's plane, giving three lines associated with $sl$, $so/sp$ and exceptional algebras correspondingly. By analyzing the partition function of refined of Chern-Simons theory, it was suggested earlier that the refinement may preserve the universality for simply laced algebras. Here we support this conjecture by analysing the Macdonald dimensions, i.e. values of Macdonald polynomials at $q^ρ$, where $ρ$ is the Weyl vector: there is a universality formula that describes these dimensions for the simply laced algebras as a function on the Vogel's plane.

hep-th↗

arXiv2022

Invariants of knots and links at roots of unity

We present a comprehensive classification of invariants of knots and links associated with irreducible representations of \uqslN{}, when the parameter of quantization $q$ is a root of unity. We demonstrate that, besides the standard HOMFLY-PT invariants, which are associated with representations with highest and lowest weights, non-trivial invariants can be associated only with nilpotent representations with parameters. We define the corresponding invariants and discuss their relations with standard invariants at particular values of parameters.

hep-th↗

arXiv2017

(q,t)-KZ equation for Ding-Iohara-Miki algebra

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. The solutions to the (q,t)-KZE are identified with the (spectral dual of) building blocks of the Nekrasov partition function for 5d linear quiver gauge theories. We also construct an elliptic version of the KZE and discuss its modular and monodromy properties, the latter being related to a dual version of KZE.

hep-th↗

arXiv2017

Check-Operators and Quantum Spectral Curves

We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach that led to constructing the (quantum) spectral curves and what is now nicknamed the EO/AMM topological recursion. We explain how the non-commutative algebra of check-operators is related to the modular kernels and how symplectic (special) geometry emerges from it in the classical (Seiberg-Witten) limit, where the quantum integrable structures turn into the well studied classical integrability. As time goes, these results turn applicable to more and more theories of physical importance, supporting the old idea that many universality classes of low-energy effective theories contain matrix model

hep-th↗

arXiv2016

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/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.

hep-th↗

arXiv2016

Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

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. We investigate the interplay between the R-matrix structure and the structure of DIM algebra intertwiners, i.e.\ of refined topological vertices and show that the R-matrix is diagonalized by the action of the spectral duality belonging to the SL(2,Z) group of DIM algebra automorphisms. We also construct the T-operators satisfying the RTT relations with the R-matrix from refined amplitudes on resolved conifold. We thus show that topological string theories on the toric Calabi-Yau threefolds can be naturally interpreted as lattice integrable models. Integrals of motion for these systems are related to q-deformation of the reflection matrices of the Liouville/Toda theories.

hep-th↗

arXiv2009

Resolving Puzzles of Massive Gravity with and without violation of Lorentz symmetry

We perform a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension. These theories are well known to possess very unusual properties, unfamiliar from studies of gauge and Lorentz invariant models. These peculiarities are caused by mixing of familiar transverse fields with revived longitudinal and pure gauge (Stueckelberg) fields and are all seen already in quadratic approximation. They are all associated with non-trivial dispersion laws, which easily allow superluminal propagation, ghosts, tachyons and essential irrationalities. Moreover, coefficients in front of emerging modes are small, what makes the theories essentially non-perturbative within a large Vainshtein radius. Attempts to get rid of unwanted degrees of freedom by giving them infinite masses lead to DVZ discontinuities in parameter (moduli) space, caused by un-permutability of different limits. Also, the condition m_{gh}=\infty can not be preserved already in non-trivial gravitational backgrounds and is unstable under any other perturbations of linearized gravity. At the same time an {\it a priori} healthy model of massive gravity in quadratic approximation definitely exists: provided by any mass level of Kaluza-Klein tower. It bypasses the problems because gravity field is mixed with other fields, and this explains why such mixing helps in other models. At the same time this can imply that the really healthy massive gravity can still require infinite number of extra fields beyond quadratic approximation.

hep-ph↗

arXiv2009

Linearized Lorentz-Violating Gravity and Discriminant Locus in the Moduli Space of Mass Terms

We analyze the pattern of normal modes in linearized Lorentz-violating massive gravity over the 5-dimensional moduli space of mass terms. Ghost-free theories arise at bifurcation points when the ghosts get out of the spectrum of propagating particles due to vanishing of the coefficient in front of ω^2 in the propagator. Similarly, the van Dam-Veltman-Zakharov (DVZ) discontinuities in the Newton law arise at another type of bifurcations, when the coefficient vanishes in front of \vec k^2. When the Lorentz invariance is broken, these two kinds of bifurcations get independent and one can easily find a ghost-free model without the DVZ discontinuity in the moduli space, at least, in the quadratic (linearized) approximation.

hep-th↗

arXiv2009

CFT exercises for the needs of AGT

An explicit check of the AGT relation between the W_N-symmetry controlled conformal blocks and U(N) Nekrasov functions requires knowledge of the Shapovalov matrix and various triple correlators for W-algebra descendants. We collect simplest expressions of this type for N=3 and for the two lowest descendant levels, together with the detailed derivations, which can be now computerized and used in more general studies of conformal blocks and AGT relations at higher levels.

hep-th↗