Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity
High Energy Physics - Theory
2009-11-10 v2
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.
Keywords
Cite
@article{arxiv.hep-th/0311069,
title = {Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity},
author = {F. Nitti and M. Porrati},
journal= {arXiv preprint arXiv:hep-th/0311069},
year = {2009}
}
Comments
Minor misprints corrected.Eight references added. To appear in JHEP.34 pages, LaTeX