https://doi.org/10.1140/epjp/s13360-024-05432-4
Regular Article
Modified graviton dynamics from spin foams: the area Regge action
Perimeter Institute, 31 Caroline Street North, N2L 2Y5, Waterloo, ON, Canada
a
bdittrich@perimeterinstitute.ca
Received:
20
January
2024
Accepted:
5
July
2024
Published online:
25
July
2024
A number of approaches to 4D quantum gravity, such as holography and loop quantum gravity, propose areas instead of lengths as fundamental variables. The area Regge action, which can be defined for general 4D triangulations, is a natural choice for an action based on areas. It does indeed appear in the semi-classical limit of spin foam models. The area Regge action does, however, only lead to a discrete version of the gravitational equations of motion, if one implements constraints, that ensure that the areas are compatible with a consistent length assignment to the edges of the triangulation. The constrained version is then classically equivalent to the length Regge action, which provides a discretization of the Einstein–Hilbert action. Here we perform the first systematic analysis of the area Regge dynamics on a hyper-cubic lattice. Surprisingly, we find that the linearized area Regge action on a hyper-cubic lattice does single out the length Regge action by its scaling behaviour in the lattice constant. That is, integrating out the variables describing fluctuations in the area–length constraints one finds the linearized length Regge action plus terms of higher order in the lattice constant. This appears without any explicit implementation of the area–length constraints.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
