Non-rational su(2) cosets and Liouville field theory

2015/10/06 by Zbigniew Jaskólski, Jaskolski, Zbigniew, Paulina Suchanek +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical and Theoretical Analysis #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1510.01773

openalex publication_date 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an su(2) WZNW model with a non-rational level and a continuous spectrum based on the non-unitary hermitian representations of the chiral algebra su(2)_k. It is conjectured that for this model the continuous spectra counterpart of the Goddard-Kent-Olive (GKO) coset construction yields the Liouville and the imaginary Liouville field theories. We support the conjecture by a number of nontrivial tests based on analytic calculations.

Citations

• Conformal field theory on the plane
• Current algebra and Wess-Zumino model in two dimensions
• Infinite conformal symmetry in two-dimensional quantum field theory
• SUPERCONFORMAL 2D MINIMAL MODELS AND AN UNUSUAL COSET CONSTRUCTION
• Open Verlinde line operators

Related

• SU(2)_k Logarithmic Conformal Field Theories
• Non-Compact WZW Conformal Field Theories
• Joint Description of Periodic SL(2,R) WZNW Model and Its Coset Theories
• Canonical approach to the WZNW model
• Extended su(2)_k and restricted U_q sl(2)