Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

Abstract

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 $\mathrm{SL}(2,\mathbb{R})$ 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.

arXiv comment43 pages, 2 figures, 2 tables; published version, minor misprints corrected

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Cited by in corpus (7)

• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• The Floquet Baxterisation
• Superstrings in Thermal Anti-de Sitter Space
• Bethe ansatz inside Calogero-Sutherland models
• Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries