Quantum gravity at the corner

Laurent Freidel (1) , Alejandro Perez (2, 3)

1 Perimeter Institute for Theoretical Physics [Waterloo]
2 CPT - E4 Gravité quantique
3 CPT - Centre de Physique Théorique - UMR 7332

We investigate the quantum geometry of $2d$ surface $S$ bounding the Cauchy slices of 4d gravitational system. We investigate in detail and for the first time the symplectic current that naturally arises boundary term in the first order formulation of general relativity in terms of the Ashtekar-Barbero connection. This current is proportional to the simplest quadratic form constructed out of the triad field, pulled back on $S$. We show that the would-be-gauge degrees of freedom---arising from $SU(2)$ gauge transformations plus diffeomorphisms tangent to the boundary, are entirely described by the boundary $2$-dimensional symplectic form and give rise to a representation at each point of $S$ of $SL(2,\mathbb{R}) \times SU(2)$. Independently of the connection with gravity, this system is very simple and rich at the quantum level with possible connections with conformal field theory in 2d. A direct application of the quantum theory is modelling of the black horizons in quantum gravity.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Laurent Freidel, Alejandro Perez. Quantum gravity at the corner. Universe, 2018, 4 (10), pp.107. ⟨10.3390/universe4100107⟩. ⟨hal-01258904⟩