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Register a new userAn integrable spin chain for the SL(2,R)/U(1) black hole sigma model
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We introduce a spin chain based on finite-dimensional spin-1/2 SU(2) representations but with a non-hermitian `Hamiltonian and show, using mostly analytical techniques, that it is described at low energies by the SL(2,R)/U(1) Euclidian black hole Conformal Field Theory. This identification goes beyond the appearance of a non-compact spectrum: we are also able to determine the density of states, and show that it agrees with the formulas in [J. Math. Phys. 42, 2961 (2001)] and [JHEP 04, 014 (2002)], hence providing a direct `physical measurement of the associated reflection amplitude.
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Two branches of integrable open quantum-group invariant $D_{n+1}^{(2)}$ quantum spin chains are known. For one branch (epsilon=0), a complete Bethe ansatz solution has been proposed. However, the other branch (epsilon=1) has so far resisted solution. In an effort to address this problem, we consider here the simplest case n=1. We propose a Bethe ansatz solution, which however is not complete, as it describes only the transfer-matrix eigenvalues with odd degeneracy. We also consider a proposal for the missing eigenvalues.
This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged ${rm SL}(2,mathbb{R})$ WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.
The periodic $OSp(1|2)$ quantum spin chain has both a graded and a non-graded version. Naively, the Bethe ansatz solution for the non-graded version does not account for the complete spectrum of the transfer matrix, and we propose a simple mechanism for achieving completeness. In contrast, for the graded version, this issue does not arise. We also clarify the symmetries of bot
We study algebras and correlation functions of local operators at half-BPS interfaces engineered by the stacks of D5 or NS5 branes in the 4d $mathcal{N}=4$ super Yang-Mills. The operator algebra in this sector is isomorphic to a truncation of the Yangian $mathcal{Y}(mathfrak{gl}_n)$. The correlators, encoded in a trace on the Yangian, are controlled by the inhomogeneous $mathfrak{sl}_n$ spin chain, where $n$ is the number of fivebranes: they are given in terms of matrix elements of transfer matrices associated to Verma modules, or equivalently of products of Baxters Q-operators. This can be viewed as a novel connection between the $mathcal{N}=4$ super Yang-Mills and integrable spin chains. We also remark on analogous constructions involving half-BPS Wilson lines.
We study the SL(2,R) WZWN string model describing bosonic string theory in AdS_3 space-time as a deformed oscillator together with its mass spectrum and the string modified SL(2,R) uncertainty relation. The SL(2,R) string oscillator is far more quantum (with higher quantum uncertainty) and more excited than the non deformed one. This is accompassed by the highly excited string mass spectrum which is drastically changed with respect to the low excited one. The highly excited quantum string regime and the low excited semiclassical regime of the SL(2,R) string model are described and shown to be the quantum-classical dual of each other in the precise sense of the usual classical-quantum duality. This classical-quantum realization is not assumed nor conjectured. The quantum regime (high curvature) displays a modified Heisenbergs uncertainty relation, while the classical (low curvature) regime has the usual quantum mechanics uncertainty principle.
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