Cosmological constant in loop quantum gravity vertex amplitude
Abstract
A new q deformation of the Euclidean EPRL/FK (Engle-Pereira-Rovelli-Livine/Freidel-Krasnov) vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph [related to two copies of quantum SU(2) group at different roots of unity] embedded in a 3-sphere. We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.
- Publication:
-
Physical Review D
- Pub Date:
- September 2011
- DOI:
- 10.1103/PhysRevD.84.064010
- arXiv:
- arXiv:1105.2212
- Bibcode:
- 2011PhRvD..84f4010H
- Keywords:
-
- 04.60.Pp;
- 02.20.Uw;
- Loop quantum gravity quantum geometry spin foams;
- Quantum groups;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 6 pages, 5 figures, result and presentation improved