arXiv subjects

Tim Schuhmann

Publications and source records attributed to Tim Schuhmann.

5 recordsLinked to original sources

arXiv2026

The quadratic growth of Krylov spread complexity in the BTZ black hole

The boundary quantity that captures the growth of black-hole interiors quantified by holographic complexity remains unknown beyond 2d dilaton gravity. We provide a critical analysis of a partition-function construction of Krylov spread complexity for thermofield-double states that provides a dimension-independent boundary reconstruction from semiclassical holographic partition functions, while developing the present dynamical and bulk construction for the BTZ saddle. In the double-scaled Sachdev-Ye-Kitaev model, where exact and semiclassical results can be compared, we show that the classical limit is reliable only when taken after the complexity has been reconstructed; taking this limit at the level of individual Lanczos coefficients discards essential information. Applying the construction to a large-central-charge two-dimensional conformal field theory above the Hawking-Page temperature dual to a Ba\~nados-Teitelboim-Zanelli black hole, we find an intermediate departure from early-time quadratic growth followed by behavior compatible with a return toward asymptotically quadratic growth, rather than the linear late-time behavior of the volume and the standard finite-functional complexity = anything class. We then match this boundary behavior to a generalized complexity = anything bulk object built from an infinite series of extrinsic-curvature invariants. The construction provides a systematic route from black-hole thermodynamics to Krylov dynamics and can naturally be extended to higher-dimensional holographic black holes.

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arXiv2025

De Sitter holographic complexity from Krylov complexity in DSSYK

We utilize the recent connection between the high energy limit of the double-scaled SYK model and two-dimensional de Sitter solutions of sine dilaton gravity to identify the length of a family of geodesics spanned between future and past infinities with Krylov spread complexity. This constitutes an explicit top-down microscopic realization of holographic complexity in a cosmological spacetime. Our identification is different from the existing holographic complexity proposals for de Sitter geometries which are anchored either on horizons as holographic screens or on timelike observers. This leads us to introduce and investigate a new cosmological holographic complexity proposal in any dimension. It is based on extremal timelike volumes anchored at the asymptotic past and future and at large values of the anchoring boundary coordinate grows linearly with growth rate proportional to the product of de Sitter entropy and temperature.

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arXiv2025

Driven inhomogeneous CFT as a theory in curved space-time

For two-dimensional conformal field theories driven by evolving background space-time metrics in a closed universe, we present an operator formulation as a driven inhomogeneous CFT. The Hamiltonian of this theory is given by a background space-time dependent smearing of the stress tensor over the spatial slice. Emphasis is placed on the treatment of the curved-space Weyl anomaly, which we show is realized by the difference between Schr\"odinger and Heisenberg picture Hamiltonians once an appropriate renormalization scheme, the chirally split scheme, is chosen. As a result, the unitary evolution generated by the background metric coincides with that of a Virasoro quantum circuit. To showcase our formalism, we consider the stress tensor one-point function and the entanglement entropy of an interval in both operator and curved-space formulations. We find that these curved-space observables admit a state interpretation only in the chirally split scheme. Finally, we derive the holographic dual of the driven CFT in three-dimensional gravity, extending previous works to arbitrary driving. The holographic dictionary reproduces the stress tensor one-point function and the entanglement entropy in a diffeomorphism invariant scheme.

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arXiv2024

Krylov spread complexity as holographic complexity beyond JT gravity

One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at infinite temperature and the complexity = volume proposal in classical JT gravity. Our work utilizes the recent connection between double-scaled SYK and sine-dilaton gravity to show that the quantitative relation between Krylov spread complexity and complexity = volume extends to finite temperatures and to full quantum regime on the gravity side at disk level. From the latter we isolate the first quantum correction to the complexity = volume proposal and propose to view it as a complexity of quantum fields in the bulk. Finally, we comment on the switchback effect, whose presence would make the Krylov spread complexity a fully fledged holographic complexity at least in sine-dilaton gravity.

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arXiv2024

Towards complexity of primary-deformed Virasoro circuits

The Fubini-Study metric is a central element of information geometry. We explore the role played by information geometry for determining the circuit complexity of Virasoro circuits and their deformations. To this effect, we study unitary quantum circuits generated by the Virasoro algebra and Fourier modes of a primary operator. Such primary-deformed Virasoro circuits can be realized in two-dimensional conformal field theories, where they provide models of inhomogeneous global quenches. We consider a cost function induced by the Fubini-Study metric and provide a universal expression for its time-evolution to quadratic order in the primary deformation for general source profiles. For circuits generated by the Virasoro zero mode and a primary, we obtain a non-zero cost only if spatial inhomogeneities are sufficiently large. In this case, we find that the cost saturates when the source becomes time-independent. The exact saturation value is determined by the history of the source profile. As a byproduct, returning to undeformed circuits, we relate the Fubini-Study metric to the K\"ahler metric on a coadjoint orbit of the Virasoro group.

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