Gravitational null rays are quantized in a diffeomorphism-covariant way using the gravitational dressing time as quantum reference frame, producing a Virasoro crossed-product algebra of gauge-invariant observables.
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Covariant regulator for entanglement entropy: Proofs of the Bekenstein bound and the quantum null energy condition
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abstract
While von Neumann entropies for subregions in quantum field theory universally contain ultraviolet divergences, differences between von Neumann entropies are finite and well-defined in many physically relevant scenarios. We demonstrate that such a notion of entropy differences can be rigorously defined in quantum field theory in a general curved spacetime by introducing a novel, covariant regulator for the entropy based on the modular crossed product. This regulator associates a type II von Neumann algebra to each spacetime subregion, resulting in well-defined renormalized entropies. This prescription reproduces formulas for entropy differences that coincide with heuristic formulas widely used in the literature, and we prove that it satisfies desirable properties such as unitary invariance and concavity. As an application, we provide proofs of the Bekenstein bound and the quantum null energy condition, formulated directly in terms of vacuum-subtracted von Neumann entropies.
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Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
Convexity of non-commutative L^p norms yields bounds on relative entropy for arbitrary excitations of faithful states in general von Neumann algebras, with uniform boundedness proven for single-particle states of the chiral current.
Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro deformations to capture diffeomorphism anomalies and distinguish gauge, physical, and
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
A semiclassical construction of fiducial observers in JT gravity, fixed by conformal isometry flow, is extended to the quantum regime to compute wormhole contributions yielding finite thermal entropy and a quantum description of the stretched horizon.
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Gravitational null rays: Covariant Quantization and the Dressing Time
Gravitational null rays are quantized in a diffeomorphism-covariant way using the gravitational dressing time as quantum reference frame, producing a Virasoro crossed-product algebra of gauge-invariant observables.
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Relative entropy for $\lambda \phi^4$ in the Rindler wedge
Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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Bounding relative entropy for non-unitary excitations in quantum field theory
Convexity of non-commutative L^p norms yields bounds on relative entropy for arbitrary excitations of faithful states in general von Neumann algebras, with uniform boundedness proven for single-particle states of the chiral current.
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Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro deformations to capture diffeomorphism anomalies and distinguish gauge, physical, and
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Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
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Fiducial observers and the thermal atmosphere in the black hole quantum throat
A semiclassical construction of fiducial observers in JT gravity, fixed by conformal isometry flow, is extended to the quantum regime to compute wormhole contributions yielding finite thermal entropy and a quantum description of the stretched horizon.
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