Multiple Shocks

TL;DR

The paper investigates how chaotic CFT dynamics and scrambling shape the bulk geometry of two entangled CFTs by constructing wormholes from sequences of shock-wave Perturbations. By analyzing one-, two-, and many-shock configurations, it shows that large time separations and numerous perturbations can generate very long wormholes, suppressing local two-sided correlations as captured by geodesic probes. It also develops an ensemble framework for typical states and argues that truly typical states may not have smooth geometric duals, raising questions about ER=EPR and the nature of holographic duals for generic states. The work highlights how scrambling time t_* and boost effects govern the connectivity of the two boundaries and suggests directions for understanding typicality, backreaction, and the limits of semiclassical geometries in holography.

Abstract

Using gauge/gravity duality, we explore a class of states of two CFTs with a large degree of entanglement, but with very weak local two-sided correlation. These states are constructed by perturbing the thermofield double state with thermal-scale operators that are local at different times. Acting on the dual black hole geometry, these perturbations create an intersecting network of shock waves, supporting a very long wormhole. Chaotic CFT dynamics and the associated fast scrambling time play an essential role in determining the qualitative features of the resulting geometries.

Figures (10)

• Figure 1: The geometry dual to Eq. (\ref{['oneW']}) consists of a perturbation that emerges from the past horizon and falls through the future horizon (left). If $t_1$ is sufficiently early, the boost relative to the $t = 0$ slice generates backreaction in that frame (right). Note that the horizons no longer meet.
• Figure 2: The dual to a two-$W$ state is constructed from the one-$W$ state by adding a perturbation near the boundary at time $t_2$ and then evolving forwards and backwards.
• Figure 3: As $t_2$ shifts earlier, the time at which the original shock reaches the boundary shifts later, eventually moving onto the singularity (right).
• Figure 4: The thermofield double and the first six multi-$W$ states are drawn. In each case, the next geometry is obtained from the previous by adding a shock either from the top left or bottom left corner. The gray regions are sensitive to the details of a collision, but the white regions are not. Using the time-folded bulk of HMPS, these states can be combined as different sheets of an "accordion" geometry.
• Figure 5: A geodesic passes across a portion of the wormhole. It intersects the null boundaries of the central regions halfway across their width.