Wronskian-type formula for inhomogeneous TQ-equations

The transfer-matrix eigenvalues of the isotropic open Heisenberg quantum spin-1/2 chain with non-diagonal boundary magnetic fields are known to satisfy a TQ-equation with an inhomogeneous term. We derive here a discrete Wronskian-type formula relating a solution of this inhomogeneous TQ-equation to the corresponding solution of a dual inhomogeneous TQ-equation.Comment: 6 pages; to appear in Theor. Math. Phys. as part of the Proceedings of the CQIS-2019 workshop in St. Petersbur

Supersymmetry in the boundary tricritical Ising field theory

We argue that it is possible to maintain both supersymmetry and integrability in the boundary tricritical Ising field theory. Indeed, we find two sets of boundary conditions and corresponding boundary perturbations which are both supersymmetric and integrable. The first set corresponds to a ``direct sum'' of two non-supersymmetric theories studied earlier by Chim. The second set corresponds to a one-parameter deformation of another theory studied by Chim. For both cases, the conserved supersymmetry charges are linear combinations of Q, \bar Q and the spin-reversal operator \Gamma.Comment: 19 pages, LaTeX; amssymb, no figures; v2 one paragraph and one reference added; v3 Erratum adde

Bethe Ansatz for the open XXZ chain from functional relations at roots of unity

We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ quantum spin chain derived from functional relations obeyed by the transfer matrix at roots of unity.Comment: 10 pages, LaTeX; includes ws-procs9x6.cls and rotating_pr.sty (World Scientific proceedings style, 9 x 6 inch trim size); presented at the 23rd International Conference of Differential Geometric Methods in Theoretical Physics (DGMTP) at the Nankai Institute of Mathematics in Tianjin, China, 20-26 August 2005, and to appear in the Proceeding

Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of the boundary parameters, the Bethe Ansatz solution is formulated in terms of Jacobian elliptic functions.Comment: 14 pages, LaTeX; amssymb, no figure

Twisting singular solutions of Bethe's equations

The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.Comment: 10 pages; v2: references added; v3: introduction expanded, and more references adde

Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''

We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A^{(1)}_n$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not require that the corresponding $R$ matrix have crossing symmetry.Comment: 4 pages, plain tex, UMTG-16

q-deformed su(2|2) boundary S-matrices via the ZF algebra

Beisert and Koroteev have recently found a bulk S-matrix corresponding to a q-deformation of the centrally-extended su(2|2) algebra of AdS/CFT. We formulate the associated Zamolodchikov-Faddeev algebra, using which we derive factorizable boundary S-matrices that generalize those of Hofman and Maldacena.Comment: 15 pages; v2: correct misplaced equation labe

Wrapping corrections for non-diagonal boundaries in AdS/CFT

We consider an open string stretched between a Y=0 brane and a Y_theta=0 brane. The latter brane is rotated with respect to the former by an angle theta, and is described by a non-diagonal boundary S-matrix. This system interpolates smoothly between the Y-Y (theta =0) and the Y-bar Y (theta = pi/2) systems, which are described by diagonal boundary S-matrices. We use integrability to compute the energies of one-particle states at weak coupling up to leading wrapping order (4, 6 loops) as a function of the angle. The results for the diagonal cases exactly match with those obtained previously.Comment: 21 pages, 1 figur

Boundary energy of the open XXX chain with a non-diagonal boundary term

We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.Comment: 10 pages, 9 figures; v2: Figs 4 are improved; v3: reference added; v4: erratum adde