Related papers: Solutions to the reflection equation and integrabl…

We establish and analyze a new relationship between the matrices describing an arbitrary component of a spin $s$, where $2s\in \mathbb{Z}^+$, and the matrices of $\mathbb{C}P^{2s}$ two-dimensional Euclidean sigma models. The spin matrices…

We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N=2 superconformal field theories. We also determine the mini-versal deformation of these…

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the…

We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The…

We consider type IIA brane configurations, similar to those that realize SO(2N) supersymmetric QCD, that include orientifold planes and anti-branes. Such brane configurations lead to Sp(2N) field theories that become supersymmetric in the…

We define a superalgebra S2(N/2) as a Z2 graded algebra of dimension 2N+3, where N is a positive, odd integer. The even component is a three-dimensional abelian subalgebra, while the odd component is made up of two N-dimensional, mutually…

We present brane constructions in Type IIA string theory for N=1 supersymmetric SO and Sp gauge theories with tensor representations using an orientifold 6-plane. One limit of these set-ups corresponds to N=2 theories previously constructed…

The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified…

Seiberg-Witten theory can be embedded in F-theory using D3 branes probing an orientifold geometry. The non-perturbative corrections in the orientifold picture map directly to the instanton corrections in the corresponding gauge theory that…

We continue to investigate the relationship between the infrared physics of N=2 supersymmetric gauge theories in four dimensions and various integrable models such as Gaudin, Calogero-Moser and quantum spin chains. We prove interesting…

We investigate the spin-Brauer diagram algebra, denoted ${\bf SB}_n(\delta)$, that arises from studying an analogous form of Schur-Weyl duality for the action of the pin group on ${\bf V}^{\otimes n} \otimes \Delta$. Here ${\bf V}$ is the…

We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFT's possess perturbations which define integrable QFT's. We establish that these QFT's have local and…

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric…

We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…

We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space $\Delta \textstyle{\bigotimes \bigotimes^k V}$. Here $\Delta$ is the fundamental representation of…

The integrable XXX spin s quantum chain and the alternating $s^{1}$, $s^{2}$ ($s^{1}-s^{2}={1\over 2}$) chain with boundaries are considered. The scattering of their excitations with the boundaries via the Bethe ansatz method is studied,…

We consider M-theory on (T^2\times R^2)/Z_n with M5 branes wrapped on R^2. One can probe this background with M5 branes wrapped on T^2. The theories on the probes provide many new examples of N=2 field theories without Lagrangian…

We study integrable open boundary conditions for d(2,1;\alpha)^2 and psu(1,1|2)^2 spin-chains. Magnon excitations of these open spin-chains are mapped to massive excitations of type IIB open superstrings ending on D-branes in the AdS_3 x…

D-branes can end on orbifold planes if the action of the orbifold group includes (-1)^{F_L}. We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their worldvolume. We apply our results to gauge…

We show that the solutions of the Yang--Baxter equation invariant under the action of the Yangian $Y(sl_2)$ lead to inhomogenous vertex models. Starting from a four dimensional representation of $Y(sl_2)$ we obtain an integrable family of…