Related papers: Spinon basis for higher level SU(2) WZW models

We consider N=1, D=4 superconformal U(N)^{pq} Yang-Mills theories dual to AdS_5xS^5/Z_pxZ_q orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector…

This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…

A physical and geometrical interpretation of previously introduced tensor operator algebras of U(2,2) in terms of algebras of higher-conformal-spin quantum fields on the anti-de Sitter space AdS_5 is provided. These are higher-dimensional…

This is a proceedings article reviewing a recent combinatorial construction of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion…

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and…

We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…

We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the…

Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of…

This review is devoted to collecting some results on the high spin expansion of (minimal) anomalous dimension. Thanks to the recent rationale on integrability, planar ${\cal N}=4$ super Yang-Mills theory (or its…

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…

The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…

We find the complex structure on the dual of a complex target space. For $N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the commutator of the left and right complex structures is {\em always} integrable, and hence…

An operator basis of an effective theory with a heavy particle, subject to external gauge fields, is spanned by a particular kind of neutral scalar primary of the nonrelativistic conformal group. We calculate the characters that can be used…

This article gives a complete account of the modular properties and Verlinde formula for conformal field theories based on the affine Kac-Moody algebra sl(2) at an arbitrary admissible level k. Starting from spectral flow and the structure…

Let G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal enveloping algebra U(g). We derive a Taylor-type expansion…

Using the conformal embedding on the torus, we can express some characters of $SU(3)_3$ in terms of $SO(8)_1$ characters. Then with the help of crossing symmetry, modular transformation and factorization properties of Green functions, we…

Integrable field theories exhibit infinitely many symmetries which underlie their solvability, but the structure of these symmetries can become obscured after performing an integrable deformation such as $\TT$ or an auxiliary field…

We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer…

The exact Seiberg-Witten (SW) description of the light sector in the $N=2$ SUSY $4d$ Yang-Mills theory is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevsky (GP) solution to the elliptic Whitham equations. We…

We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or…