Loop gravity string - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review D Année : 2017

Loop gravity string

Résumé

In this work we study canonical gravity in finite regions for which we introduce a generalisation of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersuface with a boundary sphere and show how the presence of this term leads to an unprecedented type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a 3-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux and that the string stress tensor represents the two dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphisms charges of quantum geometry satisfy at each puncture a Virasoro algebra with central charge $c=3$. This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary $SU(2)$ gauge symmetry is recovered via the action of the $U(1)^3$ Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin-representation. We finally show that this symmetry is broken by the presence of background curvature.
Fichier principal
Vignette du fichier
1611.03668.pdf (677.11 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01436653 , version 1 (17-04-2018)

Identifiants

Citer

Laurent Freidel, Alejandro Perez, Daniele Pranzetti. Loop gravity string. Physical Review D, 2017, 95 (10), pp.106002. ⟨10.1103/PhysRevD.95.106002⟩. ⟨hal-01436653⟩
166 Consultations
53 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More