Bootstrap on Mellin amplitudes computes the first stringy correction to the five-point 20' correlator in N=4 SYM up to one undetermined coefficient, with flat-space limit checks and byproduct four-point results.
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A bound on chaos
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abstract
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
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A randomized quench protocol enables the first fully analog measurement of infinite-temperature OTOCs on Rydberg atom arrays, revealing information propagation lightcones.
q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.
Tensor network simulations of the Ising model on hyperbolic lattices with coordination number 7 reveal power-law boundary spin correlations in the disordered phase and logarithmic boundary entanglement entropy at criticality, consistent with holography.
Modular flow in SYK models coupled to a bath reveals singularities allowing reconstruction of bulk flow past the horizon in two-sided AdS2 black holes.
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
Unitary designs emerge from the temporal ensemble of two chaotic Hamiltonian evolutions separated by a random Pauli operation, based on the universal Pauli spectrum.
Scale-invariant open quantum systems are universally described by unparticle baths with scaling dimension d_U, producing non-Markovian kernels, a fractional Caldeira-Leggett master equation, and phase transitions at d_U = 3/2, 2, and 5/2.
Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
The traversable wormhole transmission signal in coupled SYK models persists with less than 1.1% variation after 98% random coupling deletion, showing it is controlled by inter-system coupling alone.
In TTbar-deformed anomalous CFT2 the chaos bound stays saturated while butterfly velocity depends nontrivially on deformation strength and anomaly, with a Hagedorn regime where the chaotic response turns complex.
Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-energy spectrum.
In gapped random matrix systems with parametrically many degenerate ground states, the spectral form factor at low temperatures is dominated by the disconnected contribution at all times, while the connected form factor depends only on the non-degenerate eigenvalues.
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone at the butterfly velocity because the governing dynamics reduce to FKPP domain walls.
In finite-volume massive free scalar field theory after local quench, spacing ratios of two-point function extrema follow GOE statistics and an extrema-based form factor shows RMT dip-ramp-plateau.
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
A formula maps QFT response functions under periodic sources to Einstein ring images of dual AdS black holes, with the ring radius set by the QFT total energy for Schwarzschild-AdS4.
citing papers explorer
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$20'$ Five-Point Function of $\mathcal{N}=4$ SYM and Stringy Corrections
Bootstrap on Mellin amplitudes computes the first stringy correction to the five-point 20' correlator in N=4 SYM up to one undetermined coefficient, with flat-space limit checks and byproduct four-point results.
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Information Propagation in Rydberg Arrays via Analog OTOC Calculations
A randomized quench protocol enables the first fully analog measurement of infinite-temperature OTOCs on Rydberg atom arrays, revealing information propagation lightcones.
-
q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
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Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas
LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.
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Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks
Tensor network simulations of the Ising model on hyperbolic lattices with coordination number 7 reveal power-law boundary spin correlations in the disordered phase and logarithmic boundary entanglement entropy at criticality, consistent with holography.
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Probing Evaporating Black Holes with Modular Flow in SYK
Modular flow in SYK models coupled to a bath reveals singularities allowing reconstruction of bulk flow past the horizon in two-sided AdS2 black holes.
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The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and $\mathfrak{osp}(1|2)$ Structure
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
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Quantum mechanical bootstrap without inequalities: SYK bilinear spectrum
Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
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Stochastic Krylov Dynamics: Revisiting Operator Growth in Open Quantum Systems
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
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Probing bulk geometry via pole skipping: from static to rotating spacetimes
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
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Unitary Designs from Two Chaotic Hamiltonians and a Random Pauli Operation
Unitary designs emerge from the temporal ensemble of two chaotic Hamiltonian evolutions separated by a random Pauli operation, based on the universal Pauli spectrum.
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Scale-Invariant Open Quantum Systems
Scale-invariant open quantum systems are universally described by unparticle baths with scaling dimension d_U, producing non-Markovian kernels, a fractional Caldeira-Leggett master equation, and phase transitions at d_U = 3/2, 2, and 5/2.
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Chaos-Integrability Transition in the BPS Subspace of the $\mathcal{N}=2$ SYK Model
Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
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No chaos required: traversable wormhole signals survive 98% coupling deletion
The traversable wormhole transmission signal in coupled SYK models persists with less than 1.1% variation after 98% random coupling deletion, showing it is controlled by inter-system coupling alone.
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Butterflies in $\textrm{T}\overline{\textrm{T}}$ deformed anomalous CFT$_2$
In TTbar-deformed anomalous CFT2 the chaos bound stays saturated while butterfly velocity depends nontrivially on deformation strength and anomaly, with a Hagedorn regime where the chaotic response turns complex.
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Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography
Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-energy spectrum.
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Spectral Form Factor of Gapped Random Matrix Systems
In gapped random matrix systems with parametrically many degenerate ground states, the spectral form factor at low temperatures is dominated by the disconnected contribution at all times, while the connected form factor depends only on the non-degenerate eigenvalues.
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The Maximal Entanglement Limit in Statistical and High Energy Physics
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
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Searching for emergent spacetime in spin glasses
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
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Bootstrapping transport in the Drude-Kadanoff-Martin model
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
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Entanglement spreading and emergent locality in Brownian SYK chains
In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone at the butterfly velocity because the governing dynamics reduce to FKPP domain walls.
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Random matrix theory signatures in free field theory
In finite-volume massive free scalar field theory after local quench, spacing ratios of two-point function extrema follow GOE statistics and an extrema-based form factor shows RMT dip-ramp-plateau.
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Towards a microscopic description of de Sitter dynamics
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
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Einstein Rings in Holography
A formula maps QFT response functions under periodic sources to Einstein ring images of dual AdS black holes, with the ring radius set by the QFT total energy for Schwarzschild-AdS4.
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Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
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Yang-Mills Flux Tube in AdS II: Effective String Theory
Two-loop effective string theory observables for Yang-Mills flux tubes in large-radius AdS are computed via transcendentality ansatz bootstrap, with Padé resummation used to probe interpolation toward small-radius weak-coupling AdS.
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Probing the Chaos to Integrability Transition in Double-Scaled SYK
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
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OTOC and Quamtum Chaos of Interacting Scalar Fields
Discretized λφ⁴ theory yields thermal OTOC with exponential growth and Lyapunov exponent scaling as T^{1/4}, showing quantum chaos signatures at low perturbative orders in the oscillator chain.
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Observational Tests of Regular Black Holes with Scalar Hair and their Stability
Regular black holes with phantom scalar hair are constrained by Solar System and EHT observations, with exact relations linking photon sphere Lyapunov exponent to shadow size and impact parameter.
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Complexity of Quadratic Quantum Chaos
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
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Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
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Real-Time Quantum Dynamics on the Fuzzy Sphere: Chaos and Entanglement
In this fuzzy-sphere matrix model the largest Lyapunov exponent drops to zero at finite temperature, respecting the Maldacena-Shenker-Stanford bound while entanglement shows fast scrambling.
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Holographic Brownian dynamics of a heavy particle in a boosted thermal plasma background
Holographic calculation of longitudinal and transverse diffusion coefficients for Brownian motion in a boosted AdS black brane, with verification of the fluctuation-dissipation theorem and expression of the coefficients via butterfly velocity.
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Effect of non-conformal deformation on the gapped quasi-normal modes and the holographic implications
Non-conformal deformation via Einstein-dilaton gravity increases the radius of convergence of the derivative expansion for gapped quasinormal modes of a scalar operator in the holographic dual.
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Fractionalized Fermi liquids and the cuprate phase diagram
Reviews the FL* theory for cuprates using ancilla layer models and SU(2) gauge theories to explain pseudogap hole pockets of area p/8, Fermi arcs, and transitions to d-wave superconductivity and Fermi liquid behavior.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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The Carrollian Kaleidoscope
A review summarizing Carrollian symmetries, CCFT constructions, and applications in AFS holography, Carroll hydrodynamics, and condensed matter phenomena such as fractons and flat bands.
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Quantum chaos and the holographic principle
A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.
- Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
- Universal bound on the Lyapunov spectrum of quantum master equations
- Quantum scars from holographic boson stars