Wednesday, July 27, 2011

AdS3: gravitational exclusion principle

First, it's the last day of the EPS-HEP 2011 conference in Grenoble. See live stream video here. The final plenary talks combining the continental Higgs boson searches start at 3 pm French Summer Time. See the schedule.
It seems to me that the most interesting hep-th paper today is
The Gravitational Exclusion Principle and Null States in Anti-de Sitter Space
by three bright authors - Alejandra Castro, Thomas Hartman, and Alexander Maloney. In some sense, the paper claims to "derive" the holographic principle!

By the way, on the picture, a boy created a living causal diagrammatic model of a holographic AdS3.

The simplest (invalid) reason why you would think that holography must be wrong is to construct a lot of localized states in the bulk gravitational theory: their number seemingly corresponds to a volume-extensive number of degrees of freedom (or volume-extensive entropy).

However, these three physicists show that in \(AdS_3\), there is actually a lot of (multi-particle) states that are not allowed because if you compute their (Klein-Gordon) norm, it comes out as negative or zero! If it's negative, the local bulk description must break down in some way and the full quantum gravity theory has to replace it with someone.

The case when the norm is zero is interesting as well: some infinite-dimensional symmetries related to diffeomorphisms that you could expect to be "global symmetries" generating large multiplets of physical states actually turn out to be gauge symmetries that must annihilate the physical states.

The potential of gravity to produce negative-norm states is arguably important. See Dualities vs Singularities for an example of what e.g. the negative norm of the conformal factor (overall scaling of the metric) implies.

It's been previously known that the boundary CFT description of string theory was missing some states that you would expect in quantum gravity if it were fully local and naive: this absence was dubbed stringy exclusion principle. The authors de facto offer what they think is a direct bulk (yet perturbative!) description of the same effect.

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