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

A bstract This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For model an equilibrium density matrix is proposed, which reproduces modular invariant partition function from 2001 paper of Maldacena, Ooguri Son. model, using its formulation as a gauged SL(2, ?) WZW we describe linear Hermitian structure space states also propose expression for matrix. Our analysis guided by results study certain critical, integrable spin chain. In scaling limit, latter exhibits key features including same global symmetries, algebra extended conformal symmetry continuous spectrum dimensions.