3D holography: from discretum to continuum
Abstract
We study the oneloop partition function of 3D gravity without cosmological constant on the solid torus with arbitrary metric fluctuations on the boundary. To this end we employ the discrete approach of (quantum) Regge calculus. In contrast with similar calculations performed directly in the continuum, we work with a boundary at finite distance from the torus axis. We show that after taking the continuum limit on the boundary — but still keeping finite distance from the torus axis — the oneloop correction is the same as the one recently found in the continuum in Barnich et al. for an asymptotically flat boundary. The discrete approach taken here allows to identify the boundary degrees of freedom which are responsible for the nontrivial structure of the oneloop correction. We therefore calculate also the HamiltonJacobi function to quadratic order in the boundary fluctuations both in the discrete setup and directly in the continuum theory. We identify a dual boundary field theory with a Liouville type coupling to the boundary metric. The discrete setup allows again to identify the dual field with degrees of freedom associated to radial bulk edges attached to the boundary. Integrating out this dual field reproduces the (boundary diffeomorphism invariant part of the) quadratic order of the HamiltonJacobi functional. The considerations here show that bulk boundary dualities might also emerge at finite boundaries and moreover that discrete approaches are helpful in identifying such dualities.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2016
 DOI:
 10.1007/JHEP03(2016)208
 arXiv:
 arXiv:1511.05441
 Bibcode:
 2016JHEP...03..208B
 Keywords:

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