Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity

Details Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity

2003-11-07

arxiv.org/abs/hep-th/0311069v2

JHEP 0401 (2004) 028

Physics

High Energy Physics

High Energy Physics - Theory

Minor misprints corrected.Eight references added. To appear in JHEP.34 pages, LaTeX

Scientific paper

10.1088/1126-6708/2004/01/028

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.

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