Stringy effects in scrambling (1412.6087v3)

Abstract: In [1] we gave a precise holographic calculation of chaos at the scrambling time scale. We studied the influence of a small perturbation, long in the past, on a two-sided correlation function in the thermofield double state. A similar analysis applies to squared commutators and other out-of-time-order one-sided correlators [2-4]. The essential bulk physics is a high energy scattering problem near the horizon of an AdS black hole. The above papers used Einstein gravity to study this problem; in the present paper we consider stringy and Planckian corrections. Elastic stringy corrections play an important role, effectively weakening and smearing out the development of chaos. We discuss their signature in the boundary field theory, commenting on the extension to weak coupling. Inelastic effects, although important for the evolution of the state, leave a parametrically small imprint on the correlators that we study. We briefly discuss ways to diagnose these small corrections, and we propose another correlator where inelastic effects are order one.

• The paper’s main contribution is integrating stringy corrections into holographic chaos models, thereby modifying traditional scrambling time predictions.
• It employs AdS/CFT techniques to analyze high-energy scattering near black hole horizons, demonstrating elastic string effects on correlator decay.
• The study refines quantum information theory by showing that string corrections delay the spread of chaos, impacting black hole entropy and information retention.

Elucidation of "Stringy Effects in Scrambling"

The paper "Stringy effects in scrambling" by Stephen H. Shenker and Douglas Stanford explores sophisticated alterations to chaos as depicted by holographic calculations, mainly focusing on string theoretic and Planckian influences beyond traditional Einstein gravity. The paper centers on out-of-time-order correlators using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, implicating high-energy scattering mechanisms near the event horizon of AdS black holes.

Summary and Analysis

The main contribution of the paper is the examination of stringy corrections to quantum chaos in holographic models. The authors extend prior work that relied on Einstein gravity by integrating stringy and Planckian effects that alter the dynamics of chaos at the scrambling time. Specifically, they consider elastic stringy effects which mitigate the spread of chaos and, indicatively, smooth the correlator decorrelation across scales. An unanticipated result is that these stringy effects delay disorder in boundary field theory correlators, introducing modifications to the scrambling time.

The calculations rest on analyzing high-energy particle collisions in a black hole's vicinity using the AdS/CFT framework. At this intersection of strong gravitational fields, the classical regime of Einstein gravity transitions into regions where string theoretic effects gain traction, as expressed by variations in scattering amplitudes and longitudinal spreading of strings. Elastic string corrections reshape the chaos landscape, whereas inelastic influences, notwithstanding their importance for black hole physics, impose a parametrically smaller fingerprint on the computed correlators.

Numerical Insights and Bold Claims

The paper posits a revised scrambling time, which factors as:

$$t_* = \frac{\beta}{2\pi}\left[1 + \frac{d(d-1)\ell_s^2}{4\ell_{AdS}^2}+...\right] \log S$$

where this correction signifies the first terms in the stringy expansion. Significantly, the analytical expressions suggest a slower degradation of correlators due to stringy effects, challenging prior Einstein-dominated predictions and offering a refined understanding of quantum information dispersion in holographic models.

The authors provide a meticulous comparison against prior models and emphasize the limited role of inelastic scattering in affecting out-of-time-order correlators, underscoring a nuanced comprehension of chaos propagation in AdS black holes.

Theoretical and Practical Implications

The theoretical implications pivot on improved insight into scrambling, potentially contributing to discussions on quantum information retention in black hole horizons and entropic bounds. Practically, these insights inform quantum gravity calculations, where understanding perturbative and non-linear effects has implications for fields beyond theoretical physics, including quantum computing and complex systems.

Speculation on Future AI Developments

Looking forward, the research could parallel advances in AI, where understanding the nuanced boundaries of information propagation mirrors the computational dynamics of artificial systems. Theoretical enhancements on chaos scrambling can inform the robustness of quantum algorithms that rely on entangled states—ensuring fidelity over intricate interactions. As AI models increasingly emulate complex systems, insights from quantum chaos could underpin the development of AI architectures resilient to informational degradation.

In conclusion, Shenker and Stanford's investigation bridges past foundational concepts in quantum gravity with innovative evaluations of stringy effects, significantly advancing the dialogue on information scrambling and chaos. This detailed scrutiny of string corrections invites further exploration into the quantum domain, enhancing our grasp of cosmological phenomena and symmetric dualities in theoretical physics.