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## Trigonometric degeneration and orbifold Wess-Zumino-Witten model. I.

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

Takebe T.

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.

Takebe T., , in : Progress in Mathematics. 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. P. 205-224.

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 ...

Added: August 14, 2014

Takebe T., Kuroki G., Journal of Physics A: Mathematical and Theoretical 2001 Vol. 34 No. 11 P. 2403-2413

We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonisation technique. ...

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

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., / 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

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

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

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

Netay I. V., Савватеев А. В., / Cornell University. Series math "arxiv.org". 2016.

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles.
We call them Sharygin triangles.
It turns out that they are parametrized by an open subset of an elliptic curve.
Also we prove that there are infinitely many non-similar integer ...

Added: October 19, 2016

Brown F., / arxive. Series math "nt". 2013. No. arXiv:1110.6917v2.

Abstract. We study the de Rham fundamental group of the configuration space
E (n) of n + 1 marked points on a complex elliptic curve E, and define multiple
elliptic polylogarithms. These are multivalued functions on E (n) with unipotent
monodromy, and are constructed by a general averaging procedure. We show
that all iterated integrals on E (n) , ...

Added: May 14, 2014

Brown F., Levin A., / Cornell University. Series arXiv "math". 2013. No. 1110.6917 [.

Abstract. We study the de Rham fundamental group of the configuration sp ace of several marked points on a complex elliptic curve, and define multiple elliptic polylogarithms. These are multivalued functions with unipotent monodromy, and are constructed by a general averaging proce dure. We show that all iterated integrals on this configuration space can be ...

Added: October 4, 2013

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

Lebedev P. A., Nesterenko A., Черновик статьи 2014

В работе предложен алгоритм вычисления явного вида эндоморфизма эллиптической кривой, который может использоваться для ускорения операций по вычислению кратной точки. Приведены детали авторской реализации и результаты её производительности. В статье впервые представлены решения поставленной задачи для степени соответствующего многочлена Гильберта выше пятой. ...

Added: October 23, 2014

Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2012. No. 57/12.

In this work we investigate the action of generalized Schlesinger transformation on the isomonodromic families of meromorphic connections on the linear bundles of rank two and degree zero over an elliptic curve. The main interest is the action of the gauge transformation on the moduli space of vector bundles. the central result is the explicit ...

Added: March 31, 2014

Poberezhny V. A., Matveeva A., Journal of Geometry and Physics 2017 Vol. 114 P. 384-393

We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is ...

Added: October 26, 2016

Bogomolov F. A., Fu H., European Journal of Mathematics 2018 Vol. 4 No. 2 P. 555-560

We construct pairs of elliptic curves over number fields with large intersection of projective torsion points. ...

Added: September 13, 2018

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

Pavlov A., Mathematische Zeitschrift 2021 No. 297 P. 223-254

We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain HomHom spaces in the bounded derived category Db(X). In the simplest case of a smooth elliptic curve E embedded in P2 as a smooth cubic, we get explicit values for Betti ...

Added: October 31, 2020

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., 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

Buff X., Goncharuk Nataliya, Journal of Modern Dynamics 2015 Vol. 9 P. 169-190

We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let f: R/Z -> R/Z be a (real) analytic orientation preserving circle diffeomorphism and let omega in C/Z be a parameter with positive imaginary part. Construct a complex torus by glueing the two boundary components of the annulus { z ...

Added: October 10, 2013

Brown F., / arxive. Series math "nt". 2013. No. 1110.6917.

Abstract. We study the de Rham fundamental group of the configuration space
E (n) of n + 1 marked points on a complex elliptic curve E, and define multiple
elliptic polylogarithms. These are multivalued functions on E (n) with unipotent
monodromy, and are constructed by a general averaging procedure. We show
that all iterated integrals on E (n) , ...

Added: May 14, 2014