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- Mass and Tension (momentum) Sum Rules in AdS (dS)

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PIRSA Number:

12110042

The stress-energy tensor in a conformal field theory has

zero trace.

Hence AdS boundary stress-tensors are traceless by

construction, to match this property of the dual CFT. An elegant (aka nifty)

construction based on the conformal isometry of AdS will be presented which

shows that in an asymptotically AdS spacetime, the sum of the ADM mass and the

ADM tensions is zero. This result follows strictly from the gravitational point

of view- that is, the Einstein equations and the definitions of the ADM

charges. Further, it turns out that perturbative stress-energy sources in an asymptotically

AdS spacetime must satisfy a local version of this constraint, namely that the

sum of the energy density minus the pressures equals zero. The situation with

positive cosmological constant is both similar and distinct in interesting

ways, which will be briefly discussed. The analogous (analytically continued)

conformal isometry in dS is the root of the

``k^4 “ power spectrum for causal cosmological

perturbations. Work in progress (speculations) will be presented about a

corresponding sum-rule for gravitational charges defined at future infinity in

a spacetime that approaches dS at late times.

©2012 Perimeter Institute for Theoretical Physics