2018/04/30 by Wolfgang Wieland
Physics and Astronomy · #Boundary conformal field theory #Boundary value problem #Conformal field theory #General relativity #Group field theory #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Primary field #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics #Quantum field theory #Quantum gravity #Spin foam #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep10(2018)089
published as JHEP (2018) 2018: 89 · 28 pages
openalex created_date 2018/09/27 · openalex publication_date 2018/10/01 · arxiv created 2018/10/16 · arxiv updated 2018/10/22 · openalex updated_date 2026/08/05
A bstract In this paper, we will make an attempt to clarify the relation between three-dimensional 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 one-dimensional cross section of the boundary has a discrete spectrum. In addition, we will introduce a new class of coherent states, study the quasi-local observables that generate the quasi-local Virasoro algebra and discuss some strategies to evaluate the partition function of the theory.