Localized states in global AdS space

Berenstein, David; Simón, Joan

doi:10.1103/physrevd.101.046026

Cited by 12 publications

(13 citation statements)

References 41 publications

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“…We would like to stress how the large-N limit of the AdS/CFT correspondence allows us to circumvent the technical difficulty of computing the complexity variation between states in the strongly coupled boundary CFT. Using the isomorphism between Hilbert spaces [98][99][100][101][102] i.e., the vacuum state |0 and the Hilbert space spanned with a set of free field annihilationâ n and creationâ † n operators (see below), we can perform both calculations in the bulk, as we will describe in detail in future sections, providing a much more detailed account of our earlier results in [1].…”

Section: )mentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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We investigate the first law of complexity proposed in [1], i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

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Section: )mentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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“…Classical chaos in AdS/CFT. In the context of the AdS/CFT correspondence, CFT perturbations e iO |ψ generated by operators O with large conformal dimension can be described by freely falling particles in the bulk geometry dual to |ψ , in the semiclassical approximation [51][52][53][54][55][56]. At high energies, the bulk geometry involves a black hole with the temperature related to the energy of the state by the usual thermodynamic relation.…”

Section: Jhep05(2020)071mentioning

confidence: 99%

On operator growth and emergent Poincaré symmetries

Magán

Simón

2020

J. High Energ. Phys.

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We consider operator growth for generic large-N gauge theories at finite temperature. Our analysis is performed in terms of Fourier modes, which do not mix with other operators as time evolves, and whose correlation functions are determined by their two-point functions alone, at leading order in the large-N limit. The algebra of these modes allows for a simple analysis of the operators with whom the initial operator mixes over time, and guarantees the existence of boundary CFT operators closing the bulk Poincaré algebra, describing the experience of infalling observers. We discuss several existing approaches to operator growth, such as number operators, proper energies, the many-body recursion method, quantum circuit complexity, and comment on its relation to classical chaos in black hole dynamics. The analysis evades the bulk vs boundary dichotomy and shows that all such approaches are the same at both sides of the holographic duality, a statement that simply rests on the equality between operator evolution itself. In the way, we show all these approaches have a natural formulation in terms of the Gelfand-Naimark-Segal (GNS) construction, which maps operator evolution to a more conventional quantum state evolution, and provides an extension of the notion of operator growth to QFT.

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“…energy k when one adds some Fourier mode of φ on the boundary. This reasoning is analogous to the analysis in [50] (see also [51]). Such a statement assumes that backreaction is effectively neglected; as described in [49], this means that no descendants have been excited.…”

Section: Subleading Behavior Via Cftmentioning

confidence: 60%

Aspects of Holography in Conical $AdS_3$

Berenstein¹,

Grabovsky²,

Li³

2022

Preprint

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We study the Feynman propagator of free scalar fields in AdS 3 with a conical defect. The propagator is built by solving the bulk equation of motion, summing over the modes of the field, and taking the boundary limit. We then perform several consistency checks. In the dual CFT, the operator responsible for the defect creates a highly excited state. We consider the exchange of the Virasoro identity block in the heavy-light limit to obtain an expression for the propagator sensitive to the mass of the defect. In AdS 3 /Z n , we treat the propagator by the method of images and in the geodesic approximation. More generally, we argue that long-range correlations of the scalar are suppressed as the defect becomes more massive: we find a continuous phase transition in the correlator at the BTZ threshold and examine its critical behavior. Finally, we apply our results to holographic entanglement entropy using an analogy between our scalars and replica twist fields.

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Localized states in global AdS space

Cited by 12 publications

References 41 publications

Aspects of the first law of complexity

Aspects of the first law of complexity

On operator growth and emergent Poincaré symmetries

Aspects of Holography in Conical $AdS_3$

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