Boundary K-matrices for the XYZ, XXZ AND XXX spin chains

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 explicitly derived, finding families dependig on several continuous as well as discrete parameters.Comment: 13 page

Strings in Plane Wave Backgrounds Revisited

String theory in an exact plane wave background is explored. A new example of singularity in the sense of string theory for nonsingular spacetime metric is presented. The 4-tachyon scattering amplitude is constructed. The spectrum of states found from the poles in the factorization turns out to be equivalent to that of the theory in flat space-time. The massless vertex operator is obtained from the residue of the first order pole.Comment: 15 pages, GTCRG-8, RevTe

Universal aspects of string propagation on curved backgrounds

String propagation on D-dimensional curved backgrounds with Lorentzian signature is formulated as a geometrical problem of embedding surfaces. When the spatial part of the background corresponds to a general WZW model for a compact group, the classical dynamics of the physical degrees of freedom is governed by the coset conformal field theory SO(D-1)/SO(D-2), which is universal irrespective of the particular WZW model. The same holds for string propagation on D-dimensional flat space. The integration of the corresponding Gauss-Codazzi equations requires the introduction of (non-Abelian) parafermions in differential geometry.Comment: 15 pages, latex. Typo in Eq. (2.12) is corrected. Version to be published in Phys. Rev.

Multi-Magnon Scattering in the Ferromagnetic XXX-Model with Inhomogeneities

We determine the transition amplitude for multi-magnon scattering induced through an inhomogeneous distribution of the coupling constant in the ferromagnetic XXX-model. The two and three particle amplitudes are explicitely calculated at small momenta. This suggests a rather plausible conjecture also for a formula of the general n-particle amplitude.Comment: 21 pages, latex, no figure

Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain

We analysis the symmetries of the reflection equation for open $XYZ$ model and find their solutions $K^{\pm}$ case by case. In the general open boundary conditions, the Lax pair for open one-dimensional $XYZ$ spin-chain is given.Comment: LaTeX, 17 pages, errors in references correcte

Integrable boundary conditions for classical sine-Gordon theory

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line $x\leq 0$ with local boundary condition at the origin is considered. The most general form of this boundary condition is found such that the problem be integrable. For the resulting system an infinite number of involutive integrals of motion exist. These integrals are calculated and one is identified as the Hamiltonian. The results found agree with some recent work of Ghoshal and Zamolodchikov.Comment: 10 pages, DTP/94-3

Back Reaction of Strings in Self-Consistent String Cosmology

We compute the string energy-momentum tensor and {\bf derive} the string equation of state from exact string dynamics in cosmological spacetimes. $1+1,~2+1$ and $D$-dimensional universes are treated for any expansion factor $R$. Strings obey the perfect fluid relation $p = (\gamma -1) \rho$ with three different behaviours: (i) {\it Unstable} for $R \to \infty$ with growing energy density $\rho \sim R^{2-D}$, {\bf negative} pressure, and $\gamma =(D-2)/(D-1)$; (ii){\it Dual} for $R \to 0$, with $\rho \sim R^{-D}$, {\bf positive} pressure and $\gamma = D/(D-1)$ (as radiation); (iii) {\it Stable} for $R \to \infty$ with $\rho \sim R^{1-D}$, {\bf vanishing} pressure and $\gamma = 1$ (as cold matter). We find the back reaction effect of these strings on the spacetime and we take into account the quantum string decay through string splitting. This is achieved by considering {\bf self-consistently} the strings as matter sources for the Einstein equations, as well as for the complete effective string equations. String splitting exponentially suppress the density of unstable strings for large $R$. The self-consistent solution to the Einstein equations for string dominated universes exhibits the realistic matter dominated behaviour $R \sim (X^0)^{2/(D-1)}\;$ for large times and the radiation dominated behaviour $R \sim (X^0)^{2/D}\;$ for early times. De Sitter universe does not emerge as solution of the effective string equations. The effective string action (whatever be the dilaton, its potential and the central charge term) is not the appropriate framework in which to address the question of string driven inflation.Comment: 29 pages, revtex, LPTHE-94-2

Alternating spin chains with singlet ground states

We investigate low-energy properties of the alternating spin chain model composed of spin $s_1$ and $s_2$ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3) non-linear sigma model in order to take into account quantum fluctuations. Analyzing the topological term in the resulting sigma model, we discuss how the massless or massive excitations are developed, especially according to the topological nature of the alternating spin system.Comment: 9 pages, revtex, to appear in PR

On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory

The Bethe equations, arising in description of the spectrum of the dilatation operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are considered in the anti-ferromagnetic regime. These equations are deformation of those for the Heisenberg XXX magnet. It is proven that in the thermodynamic limit roots of the deformed equations group into strings. It is proven that the corresponding Yang's action is convex, which implies uniqueness of solution for centers of the strings. The state formed of strings of length (2n+1) is considered and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that non-analyticity of the left hand side of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. Whence it is concluded that the structure of the anti-ferromagnetic vacuum is determined by the behaviour of exponential corrections to string solutions in the thermodynamic limit and possibly involves strings of length 2.Comment: LaTex, 9 pages, 1 figur