Article,
The Gravitational Exclusion Principle and Null States in Anti-de Sitter Space
(Jul 26, 2011)
Abstract
The holographic principle implies a vast reduction in the number of degrees
of freedom of quantum gravity. This idea can be made precise in AdS\_3, where
the the stringy or gravitational exclusion principle asserts that certain
perturbative excitations are not present in the exact quantum spectrum. We show
that this effect is visible directly in the bulk gravity theory: the norm of
the offending linearized state is zero or negative. When the norm is negative,
the theory is signaling its own breakdown as an effective field theory; this
provides a perturbative bulk explanation for the stringy exclusion principle.
When the norm vanishes the bulk state is null rather than physical. This
implies that certain non-trivial diffeomorphisms must be regarded as gauge
symmetries rather than spectrum-generating elements of the asymptotic symmetry
group. This leads to subtle effects in the computation of one-loop determinants
for Einstein gravity, higher spin theories and topologically massive gravity in
AdS\_3. In particular, heat kernel methods do not capture the correct spectrum
of a theory with null states.
