D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.
Holographic Krylov Complexity for Charged, Composite and Extended Probes
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We study the holographic spread/Krylov complexity of operators with non-trivial internal structure and of genuinely extended operators. We first consider a massive particle in AdS$_5\times S^5$ carrying conserved $R$-charge, and show how motion in the internal space modifies the complexity growth, yielding a natural holographic realisation of symmetry-resolved Krylov complexity. We then move to probes that are effectively pointlike from the field-theory viewpoint but possess an intrinsic structure in the bulk: baryon-vertex configurations and giant gravitons. Our results indicate that, for this broad class of structured but pointlike probes, the leading large-time behaviour retains the characteristic form expected for local operators in conformal theories, while the internal structure and induced charges produce informative subleading effects. We also study a genuinely extended probe, a fundamental string falling in AdS while stretched along a spatial direction, as a model for the spread complexity of a non-local operator. In this case, although the leading behaviour still exhibits the expected growth pattern, the subleading terms and intermediate regimes differ qualitatively from those of pointlike probes. This provides concrete evidence that extended operators carry a finer notion of spread complexity, sensitive to their spatial structure. Our results broaden the class of probes for which holographic Krylov complexity can be analysed explicitly, clarify which features are universal and which depend on the nature of the operator, and open a promising route toward a sharper field-theory understanding of complexity for charged, composite and extended excitations.
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hep-th 8years
2026 8roles
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Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
Krylov complexity's Taylor coefficients recursively determine all Lanczos coefficients, making it a complete descriptor of operator dynamics, with caveats for spread complexity.
In reduced BMN matrix models, Lanczos coefficients scale linearly with the mass parameter, producing quadratic corrections to early-time Krylov complexity growth at the same order for both state and operator versions.
Protected and few-body sectors in N=4 SYM exhibit integrable Krylov dynamics with a_n=2Mg and b_n→Mg, insufficient for testing gravitational universality of complexity growth; a finite-density program is proposed to test dependence only on coarse thermodynamic data.
An analytical method is presented to calculate Lanczos coefficients governing Krylov complexity in the reduced pulsating fuzzy sphere version of the BMN matrix model for large and small deformations.
In the BMN matrix model and its holographic duals, Krylov basis states and Lanczos coefficients are uniquely fixed by the model's mass parameter.
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Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
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Krylov Complexity for Plane Wave Matrix Model
In reduced BMN matrix models, Lanczos coefficients scale linearly with the mass parameter, producing quadratic corrections to early-time Krylov complexity growth at the same order for both state and operator versions.
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On the Universality of Probe Complexity in $\mathcal{N}=4$ SYM
Protected and few-body sectors in N=4 SYM exhibit integrable Krylov dynamics with a_n=2Mg and b_n→Mg, insufficient for testing gravitational universality of complexity growth; a finite-density program is proposed to test dependence only on coarse thermodynamic data.
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