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

TL;DR

This work shows that the gravitational exclusion (or stringy exclusion) principle in AdS${}_3$ arises from the bulk perturbative spectrum: boundary gravitons can have zero or negative norm, leading to null or nonunitary multiparticle states that must be removed. By computing norms via Brown-Henneaux charges, the authors connect bulk symplectic structure to Virasoro and ${\cal W}_N$ algebras, explaining why heat-kernel determinants overcount states and how the correct positive-norm spectrum saturates the holographic bound. The framework extends to higher-spin theories, supersymmetric cases, and chiral gravity, clarifying when and how the holographic density of states is achieved and reconciled with known dual CFTs. Overall, the paper provides a bulk mechanism for state removal that aligns perturbative spectra with holographic entropy limits and clarifies the role of null/negative-norm states across 3D gravity theories. The results also explain discrepancies between traditional one-loop computations and black-hole physics by identifying which states should be excluded from the spectrum.

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.