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We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with…

High Energy Physics - Theory · Physics 2009-10-31 Seiji Terashima , Sung-Kil Yang

We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…

Mathematical Physics · Physics 2023-04-20 Guang-Liang Li , Junpeng Cao , Xiao-Tian Xu , Kun Hao , Pei Sun , Tao Yang , Wen-Li Yang

The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous)…

High Energy Physics - Theory · Physics 2009-10-30 A. Gorsky , A. Marshakov , A. Mironov , A. Morozov

The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…

High Energy Physics - Theory · Physics 2009-08-03 W. Galleas

We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection…

Mathematical Physics · Physics 2015-09-01 Gus Schrader

We find exact solutions for N=2 supersymmetric SO(N), N=7,9,10,11,12 gauge theories with matter in the fundamental and spinor representation. These theories, with specific numbers of vectors and spinors, arise naturally in the…

High Energy Physics - Theory · Physics 2009-10-30 Mina Aganagic , Martin Gremm

Beisert et al. have identified an integrable SU(2,2) quantum spin chain which gives the one-loop anomalous dimensions of certain operators in large N QCD. We derive a set of nonlinear integral equations (NLIEs) for this model, and compute…

High Energy Physics - Theory · Physics 2008-11-26 Changrim Ahn , Rafael I. Nepomechie , Junji Suzuki

We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable…

Exactly Solvable and Integrable Systems · Physics 2010-06-22 A. V. Tsiganov

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…

High Energy Physics - Theory · Physics 2011-10-21 Kenji Muneyuki , Ta-Sheng Tai , Nobuhiro Yonezawa , Reiji Yoshioka

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

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…

Statistical Mechanics · Physics 2009-10-31 M. T. Batchelor , J. de Gier , J. Links , M. Maslen

To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken)…

High Energy Physics - Theory · Physics 2020-03-25 Davide Fioravanti , Daniele Gregori

We present simple assumptions on the constraints defining a hard core dynamics for the associated reflected stochastic differential equation to have a unique strong solution. Time-reversibility is proven for gradient systems with normal…

Probability · Mathematics 2013-06-17 Myriam Fradon

We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with $U_q(\widehat{sl_2})$. Integrable $XXZ$ spin-1 chain hamiltonian with general boundary…

High Energy Physics - Theory · Physics 2009-10-30 Takeo Inami , Satoru Odake , Yao-Zhong Zhang

We perform a systematic exact algebraic search for integrable spin-S chains which are isotropic in spin space, i.e. are su(2)-invariant. The families of spin chains found for S < 14 support recent arguments in favour of the complete…

Condensed Matter · Physics 2007-05-23 M. T. Batchelor , C. M. Yung

We construct an extended Hubbard model with open boundaries from a $R$-matrix based on the $U_q[Osp(2|2)]$ superalgebra. We study the reflection equation and find two classes of diagonal solutions. The corresponding one-dimensional open…

solv-int · Physics 2009-10-31 M. J. Martins , X. W. Guan

We consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy

We consider two-site XXX Heisenberg magnets with different boundary conditions, which are integrable systems on so(4) possessing additional cubic and quartic integrals of motion. The separated variables for these models are constructed…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 A. V. Tsiganov , O. V. Goremykin

We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains.…

Mathematical Physics · Physics 2017-03-17 N. Kitanine , J. -M. Maillet , G. Niccoli