相关论文: Elements of a Global Operator Approach to Wess-Zum…

By exploiting a correspondence between Random Regge triangulations (i.e., Regge triangulations with variable connectivity) and punctured Riemann surfaces, we propose a possible characterization of the SU(2) Wess-Zumino-Witten model on a…

In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the…

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure.…

We study the $SU(2)$ WZNW model over a family of elliptic curves. Starting from the formulation developed by Tsuchiya, Ueno and Yamada, we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard…

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…

We give an explicit description of the vector bundle of WZW conformal blocks on elliptic curves with marked points as subbundle of a vector bundle of Weyl group invariant vector valued theta functions on a Cartan subalgebra. We give a…

We review some aspects of gauged WZW models. By choosing a nilpotent subgroup as gauge group, one is lead to three main applications: the construction of field theories with an extended conformal symmetry, the construction of the effective…

We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third…

We quantize the $SU(n)$ Wess-Zumino-Witten model in terms of left and right chiral variables choosing an appropriate gauge and we compare our results with the results that have been previously obtained in the algebraic treatment of the…

Both Feynman integrals and holographic Witten diagrams can be represented as multivariable hypergeometric functions of a class studied by Gel'fand, Kapranov & Zelevinsky known as GKZ or $\mathcal{A}$-hypergeometric functions. Among other…

The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affine Lie algebra) of the WZW model, while the Einstein equations of the general non-linear…

W-algebra (of finite type) W is a certain associative algebra associated with a semisimple Lie algebra, say g, and its nilpotent element, say e. The goal of this paper is to study the category O for W introduced by Brundan, Goodwin and…

We develop a phase space path-integral approach for deriving the Lagrangian realization of the models defined by Hamiltonian reduction of the WZNW theory. We illustrate the uses of the approach by applying it to the models of non-Abelian…

We determine a fundamental solution for the differential operator (Delta - lambda_z)^n on the Riemannian symmetric space G/K, where G is any complex semi-simple Lie group, and K is a maximal compact subgroup. We develop a global zonal…

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra $\cgh$. The resulting reduced models, called {\em Generalized Non-Abelian Conformal Affine Toda…

Starting from the Virasoro algebra and its relatives the generalization to higher genus compact Riemann surfaces was initiated by Krichever and Novikov. The elements of these algebras are meromorphic objects which are holomorphic outside a…

Let $\mathfrak{g}$ be a simple finite-dimensional Lie superalgebra with a non-degenerate supersymmetric even invariant bilinear form, $f$ a nilpotent element in the even part of $\mathfrak{g}$, $\Gamma$ a good grading of $\mathfrak{g}$ for…

A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with…

The higher Sugawara operators acting on the Verma modules over the affine Kac-Moody algebra at the critical level are related to the higher Hamiltonians of the Gaudin model due to work of Feigin, Frenkel and Reshetikhin. An explicit…

To a conformal map $f$ from the disk $\mathbb{D}$ into the complex plane onto a domain with rectifiable Ahlfors-regular boundary, we associate a new kind of Grunsky operator on the Hardy space of the unit disk. This is analogous to the…