A bulk manifestation of Krylov complexity
A bulk manifestation of Krylov complexity
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS2. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS2 has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.
Rabinovici, E.
f97c4550-c0ad-4837-a529-42387151ea9d
Sánchez-Garrido, A.
6add42c4-992e-455c-a098-f26e85168537
Shir, Ruth
80e05c9b-9440-4c4d-a5b8-95cebfaa32f3
Sonner, J.
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
31 August 2023
Rabinovici, E.
f97c4550-c0ad-4837-a529-42387151ea9d
Sánchez-Garrido, A.
6add42c4-992e-455c-a098-f26e85168537
Shir, Ruth
80e05c9b-9440-4c4d-a5b8-95cebfaa32f3
Sonner, J.
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
Rabinovici, E., Sánchez-Garrido, A., Shir, Ruth and Sonner, J.
(2023)
A bulk manifestation of Krylov complexity.
JHEP, 2023, [213].
(doi:10.1007/JHEP08(2023)213).
Abstract
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS2. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS2 has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.
Text
JHEP08(2023)213
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Accepted/In Press date: 15 August 2023
Published date: 31 August 2023
Identifiers
Local EPrints ID: 501466
URI: http://eprints.soton.ac.uk/id/eprint/501466
ISSN: 1126-6708
PURE UUID: 5f00e9e1-4abc-4baf-bbf1-3b35962357aa
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Date deposited: 02 Jun 2025 16:47
Last modified: 22 Aug 2025 02:43
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Author:
E. Rabinovici
Author:
A. Sánchez-Garrido
Author:
Ruth Shir
Author:
J. Sonner
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