ﻻ يوجد ملخص باللغة العربية
We study the quantization of the corner symmetry algebra of 3d gravity associated with 1d spatial boundaries. We first recall that in the continuum, this symmetry algebra is given by the central extension of the Poincare loop algebra. At the quantum level, we construct a discrete current algebra with a $mathcal{D}mathrm{SU}(2)$ quantum symmetry group that depends on an integer $N$. This algebra satisfies two fundamental properties: First it is compatible with the quantum space-time picture given by the Ponzano-Regge state-sum model, which provides a path integral amplitudes for 3d loop quantum gravity. We then show that we recover in the $Nrightarrowinfty$ limit the central extension of the Poincare current algebra. The number of boundary edges defines a discreteness parameter $N$ which counts the number of flux lines attached to the boundary. We analyse the refinement, coarse-graining and fusion processes as $N$ changes. Identifying a discrete current algebra on quantum boundaries is an important step towards understanding how conformal field theories arise on spatial boundaries in loop quantum gravity. It also shows how an asymptotic BMS symmetry group could appear from the continuum limit of 3d quantum gravity.
Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a consequence of t
In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particles mass and the cutoff scale above which the effective description of
Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the
In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that many recent results, in
We investigate the ultraviolet behaviour of quantum gravity within a functional renormalisation group approach. The present setup includes the full ghost and graviton propagators and, for the first time, the dynamical graviton three-point function. T