Holographic description of boundary gravitons in (3+1) dimensions

Seth Asante (Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada; Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada) ; Bianca Dittrich (Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada; Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Heyendaalseweg 135, Nijmegen, 6525 AJ, The Netherlands) ; Hal Haggard (Physics Program, Bard College, 30 Campus Road, Annandale-On-Hudson, NY, 12504, U.S.A.; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada)

Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity’s holographic formulation. Holography holds promise for simplifying computations in quantum gravity. While holographic descriptions of three-dimensional spacetimes and of spacetimes with a negative cosmological constant are well-developed, a complete boundary description of zero curvature, four-dimensional spacetime is not currently available. Building on previous work in three-dimensions, we provide a new route to four-dimensional holography and its boundary gravitons. Using Regge calculus linearized around a flat Euclidean background with the topology of a solid hyper-torus, we obtain the effective action for a dual boundary theory, which describes the dynamics of the boundary gravitons. Remarkably, in the continuum limit and at large radii this boundary theory is local and closely analogous to the corresponding result in three-dimensions. The boundary effective action has a degenerate kinetic term that leads to singularities in the one-loop partition function that are independent of the discretization. These results establish a rich boundary dynamics for four-dimensional flat holography.

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Published on:
17 January 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 1
Pages 1-50
DOI:
https://doi.org/10.1007/JHEP01(2019)144
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: