The Gravitational Exclusion Principle and Null States in Anti-de Sitter Space

TL;DR

This paper explores how the holographic principle in AdS_3 leads to the exclusion of certain excitations in quantum gravity, revealing null or negative norm states that influence the theory's spectrum and gauge symmetries.

Contribution

It demonstrates that the stringy exclusion principle manifests as null or negative norm states in bulk gravity, affecting the interpretation of gauge symmetries and one-loop calculations in AdS_3.

Findings

Negative norm states indicate breakdown of effective field theory.

Null states correspond to gauge symmetries rather than physical excitations.

Heat kernel methods fail to account for null states in spectrum calculations.

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.