Holographic Local Operator Quenches in BCFTs

TL;DR

The paper addresses local operator quenches in two-dimensional BCFTs by constructing a gravity dual in AdS$_3$ with an end-of-the-world brane and a backreacting massive particle, and by performing a parallel BCFT analysis via conformal maps. The authors establish an exact large-$c$ correspondence between the holographic energy-momentum tensor and holographic entanglement entropy and their BCFT counterparts, including a careful treatment of coordinate choices and a rescaling parameter $\eta$ that effectively maps to a half-plane BCFT. Key results include explicit formulas for $T_{\pm\pm}$, the energy density, and time evolution of holographic entanglement entropy, as well as a detailed matching with BCFT computations using HHLL blocks and conformal maps; the special role of $\eta$ and the relation $\alpha_O=\chi/\kappa$ are highlighted. The study provides a tractable and consistent model linking BCFT dynamics to a gravitational dual, with implications for boundary quantum gravity and potential connections to the island formula.

Abstract

We present a gravity dual of local operator quench in a two-dimensional CFT with conformal boundaries. This is given by a massive excitation in a three-dimensional AdS space with the end of the world brane (EOW brane). Due to the gravitational backreaction, the EOW brane gets deformed in a nontrivial way. We show that the energy-momentum tensor and entanglement entropy computed from the gravity dual and from the BCFT in the large $c$ limit match perfectly. Interestingly, this comparison avoids the folding of the EOW brane in an elegant way.

Figures (18)

• Figure 1: A sketch of the coordinate transformation from the Poincare AdS into a global AdS in the presence of a massive particle (the red arrow) and an EOW brane (the red surface).
• Figure 2: Cross sections at constant $\tau$ for the backreacted geometry with a mass and a positive tension $\lambda>0$. We depicted the EOW brane as the red curved. The light green regions are the gravity duals in the AdS/BCFT. Though for $M>\frac{3}{4}R^2$, the EOW brane gets folded and the gravity dual does not make sense, we do not need this range of the mass when we consider the BCFT dual as we explain around (\ref{['relasd']}).
• Figure 3: Cross sections at constant $\tau$ for the backreacted geometry with a mass and a negative tension $\lambda<0$. We depicted the EOW branes as the red curves. The light green regions are the gravity duals of the BCFT.
• Figure 4: Time evolution of an EOW brane and a massive particle in the Poincare coordinates with $\alpha=0.1$, $\chi=0.9$ and $\lambda=2$. The vertical line is $z$ axis (the bulk direction) and the horizontal line is $x$ axis (the boundary spatial direction). The green region represents the gravity dual region of the BCFT and the red dot represents the position of the massive particle. The EOW branes attaches at the boundary at $x=0$ and $x=Z(t)$. We chose the time to be $t=0,3$ and $5$ in the left, middle and right panel. As the time evolves the EOW brane probes deeper in the bulk.
• Figure 5: The left picture sketches the setup of BCFT in the presence of the two boundaries: $x=0$ and (\ref{['disco']}). We may try to remove the right boundary by a coordinate transformation (right picture).