Related papers: Logarithmic operators in the SL(2,R) WZNW model
The key role in the derivation of the Knizhnik-Zamolodchikov equations in the $WZW$-theory is played by the energy-momentum tensor, that is constructed from a central Casimir element of the second order in a universal enveloping algebra of…
From the recently known ${\cal N}=2$ supersymmetric linear $W_{\infty}^{K,K}[\lambda]$ algebra where $K$ is the dimension of fundamental (or antifundamental) representation of bifundamental $\beta \, \gamma$ and $b \, c$ ghost system, we…
We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the…
We write the integral formula of Tarasov-Varchenko type for the solutions to the quantum Knizhnik-Zamolodchikov associated with a tensor product the of vector representations of sl_n. We consider the case where the deformation parameter q…
Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus $g$ are given. Sheaves of representations of affine Krichever-Novikov algebras over a dense open subset of the moduli space of Riemann…
In this paper, we introduce a modification of the Szasz-Mirakjan-Kantorovich operators as well as Stancu operators [9] (or a Dunkl generalization of modified Szasz-Mirakjan-Kantrovich operators [5]) which preserve the linear functions.…
We generalize local operators of the leading twist-2 of N=4 SYM theory to the case of complex Lorentz spin j using principal series representation of sl(2,R). We give the direct computation of correlation function of two such non-local…
We extend the old formalism of cut-and-join operators in the theory of Hurwitz $\tau$-functions to description of a wide family of KP-integrable {\it skew} Hurwitz $\tau$-functions, which include, in particular, the newly discovered…
Precise descriptions are given for the operator product expansion of generic primary fields as well as the factorization of four point functions as sum over intermediate states. The conjecture underlying the recent derivation of the…
Integrated time-slice correlation functions $G(t)$ with weights $K(t)$ appear, e.g., in the moments method to determine $\alpha_s$ from heavy quark correlators, in the muon g-2 determination or in the determination of smoothed spectral…
We investigate the two-logarithm matrix model with the potential $X\Lambda+\alpha\log(1+X)+\beta\log(1-X)$ related to an exactly solvable Kazakov-Migdal model. In the proper normalization, using Virasoro constraints, we prove the…
The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order…
The fractional level models are (logarithmic) conformal field theories associated with affine Kac-Moody (super)algebras at certain levels $k \in \mathbb{Q}$. They are particularly noteworthy because of several longstanding difficulties that…
We discuss the correlation functions of the SL(2,C)/SU(2) WZW model, or the CFT on the Euclidean AdS_3. We argue that their calculation is reduced to that of a free theory by taking into account the renormalization and integrating out a…
We present a proof of the one-sided $A_2$ theorem in dimension one, with a logarithmic loss. This theorem concerns one-sided Calder\'on-Zygmund operators (CZOs) whose kernels $K(x,y)$ vanish whenever $x < y$. These operators are bounded on…
We present an ansatz of generalizing the construction of recursion relations for the correlation functions of the $\mathfrak{sl}_2$-invariant fundamental exchange model in the thermodynamic limit by Jimbo, Miwa, Smirnov, Takeyama and one of…
We consider the exchange relations of screened vertex operators in the sl3 Wess-Zumino-Novikov-Witten(WZNW) model in the semiclassical limit (where level k tends to infinity). We demonstrate that the coefficients of the exchange relations…
We give a proof of Alexandrov's conjecture on a formula connecting the Kontsevich-Witten and Hodge tau-functions using only the Virasoro operators. This formula has been confirmed up to an unknown constant factor. In this paper, we show…
Two chiral aspects of the SL(2,R) WZW model in an operator formalism are investigated. First, the meaning of duality, or conjugation, of primary fields is clarified. On a class of modules obtained from the discrete series it is shown, by…
We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d $\mathcal{N}=2$ superconformal ${\rm SU}(N)$ YM theory with hypermultiplets in the symmetric and antisymmetric representations…