HIDDEN sl(2,R) SYMMETRY IN 2D CFTs AND THE WAVE FUNCTION OF 3D QUANTUM GRAVITY

2003/11/30 by Francesco Nitti, F. Nitti, Massimo Porrati +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1088/1126-6708/2004/01/028

published as JHEP 0401 (2004) 028 · Minor misprints corrected.Eight references added. To appear in JHEP.34 pages, LaTeX

openalex publication_date 2004/01/16 · arxiv created 2004/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that all two-dimensional conformal field theories possess a hidden sl(2,R) affine symmetry. More precisely, we add appropriate ghost fields to an arbitrary CFT, and we use them to construct the currents of sl(2,R). We then define a BRST operator whose cohomology defines a physical subspace where the extended theory coincides with the original CFT. We use the sl(2,R) algebra to construct candidate wave functions for 3-d quantum gravity coupled to matter, and we discuss their viability.

Citations

• 2 + 1 dimensional gravity as an exactly soluble system
• Fock representations of the affine Lie algebraA 1 (1)
• Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
• The World as a Hologram
• Black Holes and Entropy
• Dimensional Reduction in Quantum Gravity