TY - JOUR

T1 - Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

AU - Bazhanov, Vladimir V.

AU - Kotousov, Gleb A.

AU - Lukyanov, Sergei L.

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/3

Y1 - 2021/3

N2 - 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 SL(2, 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.

AB - 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 SL(2, 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.

KW - Black Holes in String Theory

KW - Field Theories in Lower Dimensions

KW - Sigma Models

UR - http://www.scopus.com/inward/record.url?scp=85102714102&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2021)169

DO - 10.1007/JHEP03(2021)169

M3 - Article

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 3

M1 - 169

ER -