?
Trigonometric degeneration and orbifold Wess-Zumino-Witten model. II.
P. 205–224.
Takebe T.
The sheaves of conformal blocks and conformal coinvariants of the twisted WZW model have a factorisation property and are locally free even at the boundary of the moduli space, where the elliptic KZ equations and the Baxter-Belavin elliptic r matrix degenerate to the trigonometric KZ equations and the trigonometric r matrix,o respectively. Etingof's construction of the elliptic KZ equations is geometrically interpreted.
In book
Vol. 237: Infinite dimensional algebras and quantum integrable systems. Papers from the 14th International Congress on Mathematical Physics Satellite Workshop held at the University of Algarve, Faro, July 21–25, 2003. , Basel: Birkhäuser, 2005.
Черепнев М. А., Gracheva S., Информационные технологии 2024 Т. 30 № 8 С. 417–424
In December 2022, an article was published about the implementation of Shor's algorithm on a quantum computer in China. In this paper, based on the experimental results of this article, some conclusions are drawn about the possibility of practical use of Shor's algorithm and similar algorithms on quantum computers to attack information security systems built ...
Added: November 4, 2024
Смирнов И. А., Черкесова Л. В., Разумов П. В. et al., Современные наукоемкие технологии 2019 Т. 1 С. 114–118
The proposed article compares the quantum factorization algorithm of Peter Shor and the factorization algorithm of the ?-John Pollard method. As is well known, the quantum algorithm for factoring Shor consists of classical and quantum parts. In the classical part, it is proposed to use the Euclidean algorithm to find the greatest common divisor of ...
Added: May 10, 2023
Черкесова Л. В., Сафарьян О. А., Смирнов И. А., Молодой исследователь Дона 2018 Т. 3 (12) С. 111–121
The paper presents the project implementation of ρ-factor Pollard factorization in C ++, which works faster than the standard algorithm by 27%, which can significantly facilitate the work in deciphering and cryptanalysis of various ciphers such as RSA ...
Added: May 9, 2023
Sergey Derkachov, Ferrando G., Olivucci E., Journal of High Energy Physics 2021 Vol. 2021 No. 12 Article 174
We present a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in d-dimensions. The eigenvectors of a fishnet lattice of length N depend on a set of N quantum numbers (uk , lk ), each associated with the rapidity and bound-state index of a lattice excitation. Each excitation is a particle in ...
Added: October 27, 2022
Gavrylenko P., Marshakov A., Stoyan A., Journal of High Energy Physics 2020 Vol. 12 Article 125
We study the relation of irregular conformal blocks with the Painlevé III3 equation. The functional representation for the quasiclassical irregular block is shown to be consistent with the BPZ equations of conformal field theory and the Hamilton-Jacobi approach to Painlevé III3. It leads immediately to a limiting case of the blow-up equations for dual Nekrasov partition ...
Added: March 24, 2022
Derkachov S. E., Olivucci E., Journal of High Energy Physics 2021 Article 146
In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory (χCFT4) arising as a double scaling limit of the γ-deformed NN = 4 SYM theory. In the planar (t’Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square ...
Added: November 25, 2021
Feigin B. L., Jimbo M., Mukhin E., Journal of Physics A: Mathematical and Theoretical 2017 Vol. 50 No. 46 Article 464001
We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors.
That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model.
We also discuss the (gl(m),gl(n)) duality of XXZ models in ...
Added: November 5, 2020
Gavrylenko P., Iorgov N., Lisovyy O., Letters in Mathematical Physics 2020 Vol. 110 No. 2 P. 327–364
We construct the general solution of a class of Fuchsian systems of rank N as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of WN-algebra with central charge c = N − 1. The simplest example is given by the tau function of the FujiSuzuki-Tsuda system, expressed as a Fourier ...
Added: August 20, 2020
Gavrylenko P., Santachiara R., Journal of High Energy Physics 2019 Vol. 2019 No. 11 P. 1–36
We present an approach that gives rigorous construction of a class of crossing invariant functions in c = 1 CFTs from the weakly invariant distributions on the moduli space \( {\mathcal{M}}_{0,4}^{\mathrm{SL}\left(s,\mathbb{C}\right)} \) of SL(2, ℂ) flat connections on the sphere with four punctures. By using this approach we show how to obtain correlation functions in the Ashkin-Teller and the Runkel- ...
Added: May 14, 2020
Смирнов С. В., Теоретическая и математическая физика 2019 Т. 199 № 2 С. 175–192
Классифицированы элементарные преобразования Дарбу–Лапласа для полудискретных и дискретных гиперболических операторов второго порядка. Доказано, что в (полу)дискретном случае, как и в непрерывном, есть два типа элементарных преобразований Дарбу–Лапласа: преобразования Дарбу, строящиеся по некоторому конкретному элементу из ядра исходного гиперболического оператора, и классические преобразования Лапласа, которые задаются самим оператором и не зависят от выбора элемента из ядра. Показано, что в дискретном случае на ...
Added: December 2, 2019
Litvinov A., Письма в Журнал экспериментальной и теоретической физики 2019 Т. 110 № 11 С. 723–726
Исследуется явление дуальности между сигма-моделями и квантовыми теориями Тоды. Сделано утверждение о том, что {gl}(n|n) аффинная теория Тоды ведет себя в режиме сильной связи как η-деформированная CP(n-1) сигма-модель, взаимодействующая с бозонным полем. ...
Added: November 22, 2019
Two-dimensional abelian BF theory in Lorenz gauge as a twisted N = (2,2) superconformal field theory
Losev A. S., Mnev P., Youmans D., Journal of Geometry and Physics 2018 Vol. 131 P. 122–137
We study the two-dimensional topological abelian BF theory in the Lorenz gauge and, surprisingly, we find that the gauged-fixed theory is a free type B twisted N = (2, 2) superconformal theory with odd linear target space, with the ghost field c being the pullback of the linear holomorphic coordinate on the target. The Q(BRST) ...
Added: October 5, 2018
Bershtein M., Gavrylenko P., Marshakov A., Journal of High Energy Physics 2018 Vol. 08 No. 108 P. 1–54
We study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of characters of these representations leads to nontrivial identities involving lattice theta-functions. We also propose a way to calculate their exact conformal blocks, expressing them for D-series in terms of ...
Added: September 11, 2018
Belavin V., Geiko R., Journal of High Energy Physics 2018 No. 112 P. 1–23
We develop a recursive approach to computing Neveu-Schwarz conformal blocks associated with n-punctured Riemann surfaces. This work generalizes the results of [1] obtained recently for the Virasoro algebra. The method is based on the analysis of the analytic properties of the superconformal blocks considered as functions of the central charge c. It consists of two main ...
Added: August 24, 2018
Losev A. S., Rosly A. A., Polubin I., Journal of High Energy Physics 2018 No. 41 P. 1–15
We compute the ultraviolet divergences in the self-dual Yang-Mills theory, both in the purely perturbative (zero instanton charge) and topologically non-trivial sectors. It is shown in particular that the instanton measure is precisely the same as the one-loop result in the standard Yang-Mills theory. ...
Added: March 28, 2018
Bershtein M., Feigin B. L., Litvinov A., Letters in Mathematical Physics 2016 Vol. 106 No. 1 P. 29–56
We study the conformal vertex algebras which naturally arise in relation to the Nakajima–Yoshioka blow-up equations. ...
Added: November 8, 2017
M.N. Alfimov, A.V. Litvinov, Journal of High Energy Physics 2015 No. 02 P. 150–162
We study integrable structure of the coset conformal field theory and define the system of Integrals of Motion which depends on external parameters. This system can be viewed as a quantization of the ILW type hierarchy. We propose a set of Bethe anzatz equations for its spectrum. ...
Added: November 7, 2017
Litvinov A., Spodyneiko L., Journal of High Energy Physics 2016 Vol. 1611 P. 1–17
We consider the problem of classification of all W algebras which commute with a set of exponential screening operators. Assuming that the W algebra has a nontrivial current of spin 3, we find equations satisfied by the screening operators and classify their solutions. ...
Added: November 7, 2017
Belavin V., Geiko R., Journal of High Energy Physics 2017 Vol. 125 P. 1–13
We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS3/CFT2 correspondence. To give such an interpretation in previous studies, certain restrictions were necessary. Our goal here is to consider a more general situation available through the worldline approximation to the dual AdS gravity. ...
Added: August 31, 2017