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## Two-dimensional abelian BF theory in Lorenz gauge as a twisted N = (2,2) superconformal field theory

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) of the gauge-fixed theory equals the total Q of type B twisted theory. This unexpected identification of two different theories opens a way for nontrivial deformations of both of these theories. (C) 2018 Elsevier B.V. All rights reserved.

Gavrylenko P., Lisovyy O., / arXiv.org. Series arXiv.org "math-ph". 2017. No. 1705.01869.

We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $\Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painlev\'e III equation of type $D_8$ (radial sine-Gordon equation). In particular, ...

Added: May 5, 2017

Gavrylenko P., Marshakov A., Journal of High Energy Physics 2014 No. 5 P. 97

We study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare couplings. The residue formulas for the third derivatives of extended prepotentials are proven, which lead to effective way of their computation, as expansion in the weak-coupling regime. We discuss also ...

Added: October 20, 2014

Bershtein M., Gavrylenko P., Marshakov A., / arXiv.org. Series arXiv.org "hep-th". 2017. No. 1705.00957.

We study twist-field representations of the W-algebras and generalize the construction of the corresponding vertex operators to D- and B-series. We demonstrate how the computation of characters of such representations leads to the nontrivial identities involving lattice theta-functions. We propose a construction of their exact conformal blocks, which for D-series express them in terms of ...

Added: May 4, 2017

Geiko R., Belavin V., / Cornell. Series 1705.10950 "hep-th". 2017.

We continue to investigate the dual description of the Virasoro conformal blocks
arising in the framework of the classical limit of the AdS 3 /CFT 2 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: June 3, 2017

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

Takebe T., International Journal of Modern Physics A 2004 Vol. 19, May suppl. P. 418-435

Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model. ...

Added: August 14, 2014

Alkalaev K. B., Geiko R., Rappoport V. B., Journal of High Energy Physics 2017 P. 1-21

We study four types of one-point torus blocks arising in the large central charge regime. There are the global block, the light block, the heavy-light block, and the linearized classical block, according to different regimes of conformal dimensions. It is shown that the blocks are not independent being connected to each other by various links. ...

Added: April 17, 2017

Gavrylenko P., Marshakov A., / Cornell University. Series "Working papers by Cornell University". 2015. No. 1507.08794.

We consider the conformal blocks in the theories with extended conformal W-symmetry for the integer Virasoro central charges. We show that these blocks for the generalized twist fields on sphere can be computed exactly in terms of the free field theory on the covering Riemann surface, even for a non-abelian monodromy group. The generalized twist ...

Added: October 14, 2015

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

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

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

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., Journal of High Energy Physics 2015 No. 09 P. 167

We study the solution of the Schlesinger system for the 4-point $\mathfrak{sl}_N$ isomonodromy problem and conjecture an expression for the isomonodromic τ-function in terms of 2d conformal field theory beyond the known N = 2 Painlevé VI case. We show that this relation can be used as an alternative definition of conformal blocks for the ...

Added: October 9, 2015

Bershtein M., Литвинов А. В., Фатеев В. А., Nuclear Physics B 2011 Vol. 847 No. 2 P. 413-459

In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In particular, we evaluate the generalization of Selberg integral obtained by insertion of parafermionic polynomial. Our result is justified by different approach based on dual representation of parafermionic ...

Added: October 23, 2014

Belavin A. A., Bershtein M., Feigin B. L. et al., Communications in Mathematical Physics 2012 P. 1-33

The recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties: one of them is the complete factorization of the coefficients of the operator product ...

Added: February 7, 2013

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

Bershtein M., Алексеев О. В., Теоретическая и математическая физика 2010 Т. 164 № 1 С. 119-140

We consider the M(2,3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes. This construction is based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We construct an algebra of ...

Added: October 23, 2014

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

Bershtein M., Tarnopolsky G. M., Belavin A. A., JETP Letters 2011 Vol. 93 No. 2 P. 51-55

The one-matrix model is considered. The generating function of the correlation numbers is defined in such a way that this function coincide with the generating function of the Liouville gravity. Using the Kontsevich theorem we explain that this generating function is an analytic continuation of the generating function of the Topological gravity. We check the ...

Added: October 23, 2014

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

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

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Borzykh D., ЛЕНАНД, 2021

Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...

Added: February 20, 2021

В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80

Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...

Added: May 3, 2017