### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 745-775 |

Number of pages | 31 |

Journal | Journal of High Energy Physics |

Volume | 8 |

Issue number | 1 |

State | Published - Jan 1 2004 |

### Fingerprint

### Keywords

- AdS-CFT and dS-CFT Correspondence
- Conformal Field Models in String Theory
- Models of Quantum Gravity

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*8*(1), 745-775.

**Hidden sl(2,ℝ) symmetry in 2d CFTs and the wave function of 3d quantum gravity.** / Nitti, Francesco; Porrati, Massimo.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 8, no. 1, pp. 745-775.

}

TY - JOUR

T1 - Hidden sl(2,ℝ) symmetry in 2d CFTs and the wave function of 3d quantum gravity

AU - Nitti, Francesco

AU - Porrati, Massimo

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

KW - AdS-CFT and dS-CFT Correspondence

KW - Conformal Field Models in String Theory

KW - Models of Quantum Gravity

UR - http://www.scopus.com/inward/record.url?scp=23144436248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23144436248&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 745

EP - 775

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

ER -