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Extending the scope of holographic mutual information and chaotic behavior

Nilanjan Sircar, Jacob Sonnenschein, Walter Tangarife

TL;DR

The paper investigates scrambling and chaotic dynamics in holographic systems beyond AdS/CFT by studying entanglement entropy disruption in three classes: non-conformal Dp-brane backgrounds, asymptotically Lifshitz black holes, and Gauss-Bonnet gravity. By computing mutual information and tracing its evolution under shock-wave perturbations, the authors extract scrambling times and analyze extremal surfaces for half-plane regions, revealing that non-conformal and Lifshitz theories largely mimic conformal behavior, while Gauss-Bonnet gravity with negative coupling exhibits anomalous cusp/discontinuities that may indicate inconsistencies. The work provides a unified holographic framework for evaluating information scrambling across diverse geometries and highlights how higher-curvature corrections can qualitatively alter chaotic dynamics. These results deepen our understanding of fast scrambling in strongly coupled field theories and offer guidance for exploring higher-derivative gravity theories in holography.

Abstract

We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black $Dp$ branes, (ii) asymptotically Lifshitz black holes, and (iii) black $AdS$ solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.

Extending the scope of holographic mutual information and chaotic behavior

TL;DR

The paper investigates scrambling and chaotic dynamics in holographic systems beyond AdS/CFT by studying entanglement entropy disruption in three classes: non-conformal Dp-brane backgrounds, asymptotically Lifshitz black holes, and Gauss-Bonnet gravity. By computing mutual information and tracing its evolution under shock-wave perturbations, the authors extract scrambling times and analyze extremal surfaces for half-plane regions, revealing that non-conformal and Lifshitz theories largely mimic conformal behavior, while Gauss-Bonnet gravity with negative coupling exhibits anomalous cusp/discontinuities that may indicate inconsistencies. The work provides a unified holographic framework for evaluating information scrambling across diverse geometries and highlights how higher-curvature corrections can qualitatively alter chaotic dynamics. These results deepen our understanding of fast scrambling in strongly coupled field theories and offer guidance for exploring higher-derivative gravity theories in holography.

Abstract

We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black branes, (ii) asymptotically Lifshitz black holes, and (iii) black solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.

Paper Structure

This paper contains 22 sections, 122 equations, 14 figures.

Table of Contents

  1. Introduction and summary
  2. Scrambling time in general geometries
  3. The butterfly effect in non-conformal backgrounds
  4. Black $Dp$-brane geometry
  5. Mutual Information in black $Dp$-brane geometries
  6. Shock wave in black $Dp$ branes and scrambling time
  7. Extremal surfaces for half plane in TFD
  8. Mutual Information in shock wave black $Dp$ brane
  9. A black hole in asymptotically Lifshitz solutions
  10. Bulk metric
  11. Mutual Information
  12. Shock wave in Lifshitz black hole and scrambling time
  13. Extremal surfaces for half plane in TFD
  14. Mutual Information in shock wave Lifshitz Black Hole
  15. Gauss-Bonnet gravity
  16. ...and 7 more sections

Figures (14)

  • Figure 1: The geometry of an eternal black hole under the perturbation of a shock wave.
  • Figure 2: Left: Examples of $I(A,B)$ for $r_H/\ell\,=\,1$, for different values of $p$. Right: Critical values of $L$ for which $I(A,B)$ vanishes, in units of temperature.
  • Figure 3: The minimal surface
  • Figure 4: $\alpha$ as a function of $\frac{r_0}{r_h}$ at any temperature.
  • Figure 5: Left: $I(A;B)$ as a function of $\alpha$ for various $p$ branes for $L= .4 \beta$. Right: $\alpha_*$ as a function of horizon radius, in units of $\ell$.
  • ...and 9 more figures