Related papers: On the $D_n$ Spin Vertex Models for Odd $n$
Exploring a mapping among $n$-state spin and vertex models on the square lattice we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be formulated in the framework of an equivalent…
This work is a continuation of paper (hep-th/9407146) where the Boltzmann weights for the N-state integrable spin model on the cubic lattice has been obtained only numerically. In this paper we present the analytical formulae for this model…
We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…
The classical spin $O(n)$ model is a model on a $d$-dimensional lattice in which a vector on the $(n-1)$-dimensional sphere is assigned to every lattice site and the vectors at adjacent sites interact ferromagnetically via their inner…
We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…
We show that the equality of 2d $\mathcal{N}$=(2,2) supersymmetric indices in Seiberg-type duality leads to a new integrable Ising-type model. The emergence of the new model is the result of correspondence between the supersymmetric $SU(2)$…
We construct new solvable vertex models based on the spin representation of the Lie algebra $B_k$. We use these models to study the algebraic structure underlying such vertex theories. We show that all the $B_k$ spin vertex models obey a…
We overcome the barrier of constructing N=4 superconformal models in one space dimension for more than three particles. The D(2,1;alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their…
Nonlinear sigma models (NLSM) in d=3 have many interesting and non-trivial features, which were explored poorly in contrast with NLSM in d=2 and d=4. We present a few results from our study of the perturbative and non-perturbative…
We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found…
The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…
We investigate the spin-statistics connection in arbitrary dimensions for hermitian spinor or tensor quantum fields with a rotationally invariant bilinear Lagrangian density. We use essentially the same simple method as for space dimension…
A simple realization of the conformal higher spin symmetry on the free $3d$ massless matter fields is given in terms of an auxiliary Fock module both in the flat and $AdS_3$ case. The duality between non-unitary field-theoretical…
Starting with a manifestly conformal ($O(d,2)$ invariant) mechanics model in $d$ space and 2 time dimensions, we derive the action for a massless spinning particle in $d$-dimensional anti-de Sitter space. The action obtained possesses both…
We study the breaking of gauge symmetry for higher spin theory on AdS_4 dual to the 3d critical O(N) vector model. It was argued that the breaking is due to the change of boundary condition for a scalar field through a loop effect and the…
We propose new types of integrable spinor models, generalizing the well known ones of: i) Nambu-Jona-Lasinio-Vaks-Larkin models, related to SU(N); ii) the Gross-Neveu models - SP(2N); and the iii) Zakharov-Mikhailov models - SO(N). We…
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
We give a simple classification of the independent $n$-point interaction vertices for bosonic higher-spin gauge fields in $d$-dimensional Minkowski space-times. We first give a characterisation of such vertices for large dimensions, $d \geq…
A two-dimensional Sp($2N$) vector model with small $\mathcal{N}=4$ superconformal symmetry is formulated, and its chiral algebra is shown to be generated by superprimary fields of even conformal weight. This vector model is the large level…