Double Local Quenches in 2D CFTs and Gravitational Force

TL;DR

This work analyzes double local quenches in 2d CFTs, focusing on joining, splitting, and operator quenches, and probes their non-linear interactions via energy density and entanglement entropy. In holographic CFTs, the authors show that the double-quench observables are typically smaller than the sum of the two single quenches, interpretable as gravitational attraction in the AdS dual, while free theories can violate this bound in certain regimes. They provide detailed holographic calculations of EE using AdS/BCFT and boundary surfaces, and compare with exact results in Dirac fermion CFT and Ising models, highlighting oscillatory EE behavior in double splitting quenches and phase transitions in holographic settings. The study clarifies how gravitational interactions between two localized excitations manifest in CFT diagnostics, offering a non-perturbative window into bulk dynamics and suggesting directions for higher-dimensional generalizations and other information-theoretic probes. Overall, the paper establishes a concrete link between double local quenches and bulk gravitational interactions, enriching the holographic understanding of non-equilibrium quantum dynamics.

Abstract

In this work we extensively study the dynamics of excited states created by instantaneous local quenches at two different points, i.e., double local quenches. We focus on setups in two dimensional holographic and free Dirac fermion CFTs. We calculate the energy stress tensor and entanglement entropy for double joining and splitting local quenches. In the splitting local quenches we find an interesting oscillating behaviors. Finally, we study the energy stress tensor in double operator local quenches. In all these examples, we find that, in general, there are non-trivial interactions between the two local quenches. Especially, in holographic CFTs, the differences of the above quantities between the double local quench and the simple sum of two local quenches tend to be negative. We interpret this behavior as merely due to gravitational force in their gravity duals.

Figures (49)

• Figure 1: The three different double local quenches are sketched: the joining local quench ((a): left), the splitting local quench ((b): middle), and the operator local quench ((c): right) in two dimensional CFTs. We choose the two points where the local quench occurs to be $x=\pm b$.
• Figure 2: A sketch of AdS/BCFT setups for AdS$_3$. A holographic CFT on $M$ (with the boundary $\partial M$) is dual to gravity on $N$. We have $\partial N=M\cup Q$ and $\partial Q = \partial M$. The left picture shows a CFT defined on $M$ with coordinate $(w,\bar{w})$ where $M$ has a single connected boundary, and its gravity dual. The right picture shows how it looks like in $(\xi,\bar{\xi})$, where $M$ is a upper half plane, and its gravity dual. The red curve is the subsystem $A$. The yellow curve and the green curve are connected geodesic and disconnected geodesic, respectively.
• Figure 3: The left figure shows how to realize a single joining quench using path integral in a (1+1)d CFT. The right figure shows the corresponding Euclidean setup. It can be mapped into an upper half plane as showed in the lower figure using (\ref{['SJQmap']}) or (\ref{['SJQmaprev']}).
• Figure 4: $\Delta S^{con}_A=S^{con}_A -S_A^{(0)}$ (blue lines) and $\Delta S^{dis}=S^{dis}_A -S_A^{(0)}$ (orange lines) after a single joining quench in a holographic CFT, where $S_A^{(0)}$ is the EE of the vacuum state. $A=[50,100]$ in the left figure and $A=[0.1,1000]$ in the right figure. We set $a=0.1$ and $c=1$. The boundary entropy $S_{bdy}$ is set to be zero.
• Figure 5: $\Delta S_A=S_A -S_A^{(0)}$ after a single joining quench in a Dirac free fermion CFT, where $S_A^{(0)}$ is the EE of the vacuum state. $A=[50,100]$ in the left figure and $A=[0.1,1000]$ in the right figure. We set $a=0.1$.