Quantum gravity at the corner

Abstract

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.

References in corpus (6)

• Isolated and dynamical horizons and their applications
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• Black hole entropy from loop quantum gravity in higher dimensions
• Generic isolated horizons in loop quantum gravity
• Non-equilibrium thermodynamics of gravitational screens

Cited by in corpus (11)

• Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Lorentz-diffeomorphism edge modes in 3d gravity
• New boundary variables for classical and quantum gravity on a null surface
• A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• Twisted geometries, twistors and conformal transformations
• 2+1D Loop Quantum Gravity on the Edge
• Sachs' free data in real connection variables
• Aspects of quantum gravity
• Gauge from holography and holographic gravitational observables