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arXiv · 0901.4048

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

Yakov Neiman
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Abstract

We argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy regularization is assumed. We note a natural dependence of the Hilbert space on a codimension-2 boundary surface. The Hilbert product is defined dynamically, in terms of transition amplitudes which are described by a path integral. We show that a canonical basis is incompatible with these assumptions, which opens the possibility for a smaller Hilbert-space dimension than canonically expected. We argue further that this dimension may decrease with surface area at constant volume, hinting at holographic area-proportionality. We draw comparisons with other approaches and setups, and propose an interpretation for the non-holographic space of graviton states at asymptotically-Minkowski null infinity.

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Yakov Neiman. 2009-11-22. Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance. https://doi.org/10.1088/0264-9381%2F26%2F24%2F245001

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