A. Lima-Santos

Support of dS/CFT correspondence from perturbations of three-dimensional spacetime

Abstract We discuss the relation between bulk de Sitter three-dimensional spacetime and the corresponding conformal field theory at the boundary, in the framework of the exact quasinormal mode spectrum. We show that the quasinormal mode spectrum corresponds exactly to the spectrum of thermal excitations of Conformal Field Theory at the past boundary I − , together with the spectrum of a Conformal Field Theory at the future boundary I + .

Reflection

We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or A1(1) model, Izergin-Korepin or A2(2) model, sl(2|1) model and the osp(2|1) model. We find that there is a general solution for A1(10) and sl(2|1) models. In both models it is a complete K-matrix with three free parameters. For the A2(2) and os(2|1) models we find three general solutions, being two complete reflection K-matrices solutions and one incomplete reflection K-matrix solution with some null entries. In both models these solutions have two free parameters. Integrable spin-1 Hamiltonians with general boundary interactions are also presented. Several reduced solutions from these general solutions are presented in the appendices.

K

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the An−1(1) affine Lie algebra. We have classified them in two classes of solutions. The first class consists of n(n−1)/2 K-matrix solutions with three free parameters. The second class are solutions that depend on the parity of n. For n odd there exist n reflection K-matrices with 2+[n/2] free parameters. It turns out that for n even there exist n/2 K-matrices with 2+n/2 free parameters and n/2 K-matrices with 1+n/2 free parameters.

-matrices for 19-vertex models

Abstract We have considered the Zamolodchikov–Fateev and the Izergin–Korepin models with diagonal reflection boundaries. In each case the eigenspectrum of the transfer matrix is determined by application of the algebraic Bethe ansatz.

An−1(1) reflection K-matrices

We consider quasi-extreme Kerr and quasi-extreme Schwarzschild–de Sitter black holes. From the known analytical expressions obtained for their quasi-normal modes frequencies, we suggest an area quantization prescription for those objects.

Algebraic Bethe Ansatz for the Zamolodchikov-Fateev and Izergin-Korepin models with open boundary conditions

The semi-classical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models. Via the off-shell method we find the spectra and eigenvectors of the N −1 independent Gaudin Hamiltonians with symmetry osp(2|1). We also show how the off-shell Gaudin equation solves the trigonometric Knizhnik-Zamolodchikov equation.

Area Quantization in Quasi-Extreme Black Holes

Abstract 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, and the Z2-graded 19-vertex models with sl(2|1) and osp(1|2) invariances. In each case the eigenspectrum is determined by application of the coordinate Bethe ansatz.

Off-shell Bethe ansatz equation for osp(2|1) Gaudin magnets

The graded reflection equation is investigated for the Uq[osp(r|2m)(1)] vertex model. We have found diagonal solutions with at the most one free parameter and non-diagonal solutions with the number of free parameters depending on the number of bosonic (r) and fermionic (2m) degrees of freedom.

Bethe ansatz solution for quantum spin-1 chains with boundary terms

The semiclassical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models for the sl(2|1)(2) R-matrix. We find the spectra and eigenvectors of the N−1 independent Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik–Zamolodchikov equations.

Reflection matrices for the Uq[osp(r|2m)(1)] vertex model

This work concerns the boundary integrability of the spin- Temperley–Lieb model. A systematic computation method is used to construct the solutions of the boundary Yang–Baxter equations. For s half-integer, a general 2s(s + 1) + 3/2 free parameter solution is presented. It turns that for s integer, the general solution has 2s(s + 1) + 1 free parameters. Moreover, some particular solutions are discussed.