Related papers: Conformal blocks, Berenstein-Zelevinsky triangles …

There exists an intriguing relation between genus zero correlation functions in the H^+_3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the…

A WZW model for the non-semi-simple D-dimensional Heisenberg group, which directly generalizes the E_{2}^{c} group, is constructed. It is found to correspond to an D-dimensional string background of plane-wave type with physical Lorentz…

We propose an abelian categorification of $\hat{Z}$-invariants for Seifert $3$-manifolds. First, we give a recursive combinatorial derivation of these $\hat{Z}$-invariants using graphs with certain hypercubic structures. Next, we consider…

We continue the study of the gl(1|1) Wess-Zumino-Witten model. The Knizhnik-Zamolodchikov equations for the one, two, three and four point functions are analyzed, for vertex operators corresponding to typical and projective representations.…

We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in…

We propose new strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten's cigar model described by the $\mathfrak{sl}(2)/\mathfrak{u}(1)$ coset and…

The ubiquitous ADE classification has induced many proposals of often mysterious correspondences both in mathematics and physics. The mathematics side includes quiver theory and the McKay Correspondence which relates finite group…

Gauged WZNW models are integrable conformal field theories. We integrate the classical \slu{} theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson…

We study the "topological gauged WZW model associated with $SU(2)/U(1)$",which is defined as the twisted version of the corresponding supersymmetric gauged WZW model. It is shown that this model is equivalent to a topological conformal…

We define a conformal reference frame, i.e., a special projection of the six-dimensional sky bundle of a Lorentzian manifold (or the five-dimensional twistor space) to a three-dimensional manifold. We construct an example, a conformal…

We describe the general features of the Neveu-Schwarz and Ramond sectors of logarithmic conformal field theories with N=1 supersymmetry. Three particular systems are examined in some detail -- D-brane recoil, a superconformal extension of…

We construct Z_M, M= 2, 3, 4, 6 orbifold models of the N=2 superconformal field theories with central charge c=3. Then we check the description of the Z_3, Z_4 and Z_6 orbifolds by the N=2 superconformal Landau-Ginzburg models with c=3, by…

We propose a generalization of the collective field theory hamiltonian, including interactions between the original bosonic collective field $w_0 (z)$ and supplementary fields ${\bar w}_j (z)$ realizing classically a $w_\infty$ algebra. The…

We consider a 4d non-linear sigma model on the coset $(\mathrm{SU}(N)_L \times \mathrm{SU}(N)_R \times \mathrm{SU}(2))/(\mathrm{SU}(N)_{L+R}\times \mathrm{U}(1))\cong \mathrm{SU}(N) \times S^2$, that features a topological…

A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by…

We study the $SU(N)$, level $1$ Wess-Zumino-Witten model, with affine primary fields as spinon fields of fundamental representation. By evaluating the action of the Yangian generators $Q_{0}^{a}, Q_{1}^{a}$ and the Hamiltonian $H_2$ on two…

In this paper we study segmented strings in AdS$_3$ coupled to a background two-form whose field strength is proportional to the volume form. By changing the coupling, the theory interpolates between the Nambu-Goto string and the $SL(2)$…

Witten recently gave further evidence for the conjectured relationship between the $A$ series of the $N=2$ minimal models and certain Landau-Ginzburg models by computing the elliptic genus for the latter. The results agree with those of the…

By use of geometrical methods of surface theory we demonstrate links of Green-Schwarz superstring dynamics with supersymmetric exactly-solvable nonlinear systems and super-WZNW models reduced in an appropriate way.

We investigate some aspects of the c=-2 logarithmic conformal field theory. These include the various representations related to this theory, the structures which come out of the Zhu algebra and the W algebra related to this theory. We try…