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

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.

17 pages

References in corpus (5)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Quantum W-symmetry in AdS_3
• Graviton 1-loop partition function for 3-dimensional massive gravity

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• Flat/AdS boundary conditions in three dimensional conformal gravity
• Conical Defects in Higher Spin Theories
• Quantizing higher-spin gravity in free-field variables
• The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
• High Spin Topologically Massive Gravity
• Unitarity Bounds in AdS_3 Higher Spin Gravity
• Classification of Boundary Gravitons in AdS${}_3$ Gravity
• Finiteness of 3D higher spin gravity Landscape
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• On one-loop partition functions of three-dimensional critical gravities