Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity
arXiv:hep-th/0311069 · doi:10.1088/1126-6708/2004/01/028
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.
arXiv commentMinor misprints corrected.Eight references added. To appear in JHEP.34 pages, LaTeX
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