Related papers: Exact solution of a supersymmetric Gaudin model
In this work we demonstrate how one can, in a generic approach, derive a set of $N$ simple quadratic Bethe equations for integrable Richardson-Gaudin (RG) models built out of $N$ spins-1/2. These equations depend only on the $N$ eigenvalues…
The elliptic Gaudin model was obtained as the Hitchin system on an elliptic curve with two fixed points. In the present paper the algebraic-geometrical structure of the system with two fixed points is clarified. We identify this system with…
The geometry of (2,1) supersymmetric sigma-models with isometry symmetries is discussed. The gauging of such symmetries in superspace is then studied. We find that the coupling to the (2,1) Yang-Mills supermultiplet can be achieved provided…
In this letter we apply the methods of our previous paper hep-th/0108045 to noncommutative fermions. We show that the fermions form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations…
We introduce a class of quantum integrable systems generalizing the Gaudin model. The corresponding algebras of quantum Hamiltonians are obtained as quotients of the center of the enveloping algebra of an affine Kac-Moody algebra at the…
The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2,R) coalgebra symmetry. By using the properties induced by such a coalgebra…
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find…
We give a detailed analysis of the superconformal fixed points of four-dimensional N=1 supersymmetric Spin(10) gauge theory with two spinors and vectors by using a-maximization procedure.
We present an efficient program for the exact diagonalization solution of the pairing Hamiltonian in spherical systems with rotational invariance based on the SU(2) quasi-spin algebra. The basis vectors with quasi-spin symmetry considered…
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…
We have constructed the quasi-exactly-solvable two-mode bosonic realizations of su(2) and su(1, 1) algebra. We derive the relations leading to the conditions for quasi-exact solvability of two-boson Hamiltonians by determining a general…
This paper is a letter-type version of hep-th/9806236. We discuss properties of non-linear equations of motion which describe higher-spin gauge interactions for massive spin-0 and spin-1/2 matter fields in 2+1 dimensional anti-de Sitter…
We study spin chains for superconformal quiver gauge theories in the moduli space of N=2 orbifolds. Independent of integrability, which is generally broken, we use the centrally extended SU(2|2) symmetry of the magnons to fix their…
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
We define a natural basis for the algebra of $\frak{gosp}(1|2n)$-invariant differential operators on the affine superspace $\mathbb{C}^{1|2n}$. We prove that these operators lie in the image of the centre of the enveloping algebra of…
A quantum superintegrable model with reflections on the 2-sphere is introduced. Its two algebraically independent constants of motion generate a central extension of the Bannai--Ito algebra. The Schrodinger equation separates in spherical…
The high spin ultracold atom models with a special form of contact interactions, i.e., the scattering lengthes in the total spin-$2,4 \cdots$ channels are equal but may be different from that in the spin-0 channel, is studied. It is found…
We demonstrate with soluble models how to employ the effective Hamiltonian approach of Lee and Suzuki to obtain all the exact eigenvalues of the full Hamiltonian. We propose a new iteration scheme to obtain the effective Hamiltonian and…
The supersymmetric solutions of N=2, D=4 minimal ungauged and gauged supergravity are classified according to the fraction of preserved supersymmetry using spinorial geometry techniques. Subject to a reasonable assumption in the…
The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the…