Conformal boundary conditions, loop gravity and the continuum
Abstract
In this paper, we will make an attempt to clarify the relation between threedimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in three spacetime dimensions the discrete spectra for the geometric boundary observables that we find in loop quantum gravity can be understood from the quantisation of a conformal boundary field theory in the continuum without ever introducing spin networks or triangulations of space. At a technical level, the starting point is the Hamiltonian formalism for general relativity in regions with boundaries at finite distance. At these finite boundaries, we choose specific conformal boundary conditions (the boundary is a minimal surface) that are derived from a boundary field theory for an SU(2) boundary spinor, which is minimally coupled to the spin connection in the bulk. The resulting boundary equations of motion define a conformal field theory with vanishing central charge. We will quantise this boundary field theory and show that the length of a onedimensional cross section of the boundary has a discrete spectrum. In addition, we will introduce a new class of coherent states, study the quasilocal observables that generate the quasilocal Virasoro algebra and discuss some strategies to evaluate the partition function of the theory.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2018
 DOI:
 10.1007/JHEP10(2018)089
 arXiv:
 arXiv:1804.08643
 Bibcode:
 2018JHEP...10..089W
 Keywords:

 Models of Quantum Gravity;
 Conformal Field Theory;
 Topological Field Theories;
 AdSCFT Correspondence;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 28 pages