Quantum Local Quench, AdS/BCFT and Yo-Yo String

TL;DR

The paper studies local quantum quenches in $1+1$-dimensional CFTs by proposing a holographic AdS/BCFT model in which two BCFTs on half-lines are joined through detaching their $Q$-surfaces to form a folded, tensionless Yo-Yo string in AdS$_3$. The string's light-like fall creates a bulk light-cone that causally deforms Ryu-Takayanagi curves, providing a gravity-side mechanism for the time evolution of entanglement entropy that exactly matches field-theory results. Time-dependent EE for an interval is computed from these deformed RT surfaces, with a precise regulator mapping $\delta=\epsilon/2$ linking bulk and boundary descriptions under the zero boundary entropy assumption. The framework connects boundary quasi-particle propagation to bulk causal structure and offers natural avenues to extend the model to nonzero boundary entropy and backreaction regimes.

Abstract

We propose a holographic model for local quench in 1+1 dimensional Conformal Field Theory (CFT). The local quench is produced by joining two identical CFT's on semi-infinite lines. When these theories have a zero boundary entropy, we use the AdS/Boundary CFT proposal to describe this process in terms of bulk physics. Boundaries of the original CFT's are extended in AdS as dynamical surfaces. In our holographic picture these surfaces detach from the boundary and form a closed folded string which can propagate in the bulk. The dynamics of this string is governed by the tensionless Yo-Yo string solution and its subsequent evolution determines the time dependence after quench. We use this model to calculate holographic Entanglement Entropy (EE) of an interval as a function of time. We propose how the falling string deforms Ryu-Takayanagi's curves. Using the deformed curves we calculate EE and find complete agreement with field theory results.

Figures (13)

• Figure 1: Holographic picture of a BCFT defined on the half-plane, $\mathcal{M}$.
• Figure 2: Two disconnected BCFT's when $T\rightarrow 0$
• Figure 3: Holographic picture for local quench; appearance of a folded string
• Figure 4: Regulators in boundary (Left) and bulk (Right).
• Figure 5: Identification of the regulators.