Non-Compact WZW Conformal Field Theories

Abstract

We discuss non-compact WZW sigma models, especially the ones with symmetric space $H^{\mathbf{C}}/H$ as the target, for $H$ a compact Lie group. They offer examples of non-rational conformal field theories. We remind their relation to the compact WZW models but stress their distinctive features like the continuous spectrum of conformal weights, diverging partition functions and the presence of two types of operators analogous to the local and non-local insertions recently discussed in the Liouville theory. Gauging non-compact abelian subgroups of $H^{\mathbf{C}}$ leads to non-rational coset theories. In particular, gauging one-parameter boosts in the $SL(2,\bC)/SU(2)$ model gives an alternative, explicitly stable construction of a conformal sigma model with the euclidean 2D black hole target. We compute the (regularized) toroidal partition function and discuss the spectrum of the theory. A comparison is made with more standard approach based on the $U(1)$ coset of the $SU(1,1)$ WZW theory where stability is not evident but where unitarity becomes more transparent.

References in corpus (1)

• String Winding in a Black Hole Geometry

Cited by in corpus (43)

• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• Operator product expansion and factorization in the $H_3^{+}$-WZNW model
• H(3)+ correlators from Liouville theory
• The non-compact elliptic genus: mock or modular
• SL(2,R)/U(1) Supercoset and Elliptic Genera of Non-compact Calabi-Yau Manifolds
• Boundary States for AdS_2 Branes in AdS_3
• H^+_3 WZNW model from Liouville field theory
• Off-center collisions in AdS_5 with applications to multiplicity estimates in heavy-ion collisions
• Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory
• The su(2)_{-1/2} WZW model and the beta-gamma system
• A Twisted Non-compact Elliptic Genus
• Non-compact String Backgrounds and Non-rational CFT
• The arboreal gas and the supersphere sigma model
• Open Strings on AdS_2 Branes
• Three-point functions and operator product expansion in the SL(2) conformal field theory
• On Solvable Time-Dependent Model and Rolling Closed String Tachyon
• PP-waves and logarithmic conformal field theories
• On the Boundary Dynamics of Chern-Simons Gravity
• Fusion rules and four-point functions in the AdS3 WZNW model
• On the Relevance of the Thermal Scalar
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• Discrete D-branes in AdS3 and in the 2d black hole
• Supergroup - extended super Liouville correspondence
• Boundary action of the H3+ model
• The abelian cosets of the Heisenberg group
• String Theory: exact solutions, marginal deformations and hyperbolic spaces
• Near-Hagedorn Thermodynamics and Random Walks - Extensions and Examples
• Free field realization of superstring theory on AdS3
• Localized Tachyons and the g_cl conjecture
• A family of solvable non-rational conformal field theories
• The WZW model on Random Regge Triangulations
• Crosscap States for Orientifolds of Euclidean AdS_3
• The BRST quantization and the no-ghost theorem for AdS_3
• Modular Bootstrap of Boundary N=2 Liouville Theory
• Black Hole - String Transition and Rolling D-brane
• On modular properties of the AdS3 CFT
• String Theory on AdS_3/Z_N
• CFT description of three-dimensional Kerr-de Sitter spacetime
• AdS2 D-branes in AdS3 spacetime
• D-branes in the Euclidean $Ad{S}_3$ and T-duality
• Non-critical string, Liouville theory and geometric bootstrap hypothesis
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality