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

Vladimir V. Bazhanov, Gleb A. Kotousov, Sergei L. Lukyanov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number169
JournalJournal of High Energy Physics
Issue number3
StatePublished - Mar 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Black Holes in String Theory
  • Field Theories in Lower Dimensions
  • Sigma Models


Dive into the research topics of 'Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain'. Together they form a unique fingerprint.

Cite this