arXiv · 0704.2895
I review discrete and continuum approaches to quantized gravity based on the covariant Feynman path integral approach.
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Herbert W. Hamber. 2009-01-19. Discrete and Continuum Quantum Gravity. https://arxiv.org/abs/0704.2895
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We develop a formalism for calculating the entanglement entropy of an arbitrary spatial region of a gravitating spacetime at a moment of time symmetry. The crucial ingredient is a path integral over embeddings of the region into the overall spacetime, interpretable as a sum over the edge modes associated with the region. We argue that this entanglement entropy can be interpreted, to leading order in Newton's constant, as the minimal generalized entropy among all regions that enclose it. This suggests a notion of ``terrestrial holography'' where regions of space can encode larger ones, in contrast to the standard form of holography, in which degrees of freedom on the celestial sphere at the boundary of the universe encode the interior.
We present the first explicit construction of the four-derivative gravitational corrections to heterotic supergravity in the non-relativistic (NR) limit. By extending the Bergshoeff-de Roo identification (BdRi) to NR backgrounds, we obtain the complete finite four-derivative completion of the bosonic gravitational sector of NR heterotic supergravity. We investigate the BdRi in the two currently known non-relativistic limits of heterotic supergravity. In the first case, corresponding to the Lescano-Osten construction, the BdRi gives rise to a gravitational SO(8) Green-Schwarz (GS) mechanism originating from the NR gauge transformation of the Kalb-Ramond field. This mechanism can be trivialized using field redefinitions, and this modification induces a GS mechanism for boost transformations. In the second case, corresponding to the Bergshoeff-Romano construction, the resulting gravitational $SO(8)$ GS mechanism cannot be trivialized, closely paralleling the relativistic heterotic theory. Our results establish a systematic framework for incorporating higher-curvature gravitational dynamics into non-relativistic heterotic backgrounds and provide a first step toward the complete higher-derivative NR heterotic theory.
We present the first formulation of linearised gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e. treats the two frames related by electric-magnetic duality on equal footing. It is well-known that four-dimensional linearised gravity belongs to a class of singleton representations of the four-dimensional conformal algebra $\mathfrak{so}(2,4)$. Our key insight is viewing this algebra as the isometry of $\text{AdS}_5$ and realising the massless spin-2 field as edge modes of a five-dimensional topological field taking values in a specific finite-dimensional representation of $\mathfrak{so}(2,4)$. The desired four-dimensional action is then found by a covariant boundary reduction procedure.