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Complexity and Momentum
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Previous work has explored the connections between three concepts -- operator size, complexity, and the bulk radial momentum of an infalling object -- in the context of JT gravity and the SYK model. In this paper we investigate the higher dimensional generalizations of these connections. We use a toy model to study the growth of an operator when perturbing the vacuum of a CFT. From circuit analysis we relate the operator growth to the rate of increase of complexity and check it by complexity-volume duality. We further give an empirical formula relating complexity and the bulk radial momentum that works from the time that the perturbation just comes in from the cutoff boundary, to after the scrambling time.
Forward citations
Cited by 3 Pith papers
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Comments on holographic spread complexity
The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.
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Resolving Black Hole Singularities in Jackiw-Teitelboim Gravity
In JT gravity, the left confining potential required by spectral discreteness makes the wormhole length turn around and plateau, allowing boundary time to run past the would-be singularity and eliminating future horizons.
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Probing the self-coherence of primordial quantum fluctuations with complexity
Complexity of formation, unlike complexity of purification, shows distinct and timescale-matching signatures of both decoherence and recoherence in a Gaussian two-field de Sitter model.
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