Energy transport in holographic junctions

TL;DR

The paper addresses energy transport across holographic conformal junctions connecting multiple 2D CFTs by modeling the junction with a tensile string that glues three $AdS_3$ bulks. Using first-order holographic perturbations, it derives explicit reflection and transmission coefficients that depend monotonically on the brane tension and shows the total transmission is bounded by an effective central charge associated with the junction. It extends the analysis to general $N$-CFT junctions and connects the results to field-theory expectations for ICFTs, including island-formula considerations for entanglement. The findings establish a new inequality linking transport coefficients to quantum-information measures and provide closed-form transport expressions in several tension regimes, offering a framework for exploring strongly coupled junction transport and potential extensions to higher dimensions or non-conformal settings.

Abstract

We study energy transport in a conformal junction connecting three 2D conformal field theories using the AdS/CFT correspondence. The holographic dual consists of three AdS$_3$ spacetimes joined along the worldsheet of a tensile string anchored at the junction. Within a specific range of string tension, where the bulk solution is uniquely determined, we find that all energy reflection and transmission coefficients vary monotonically with the string tension. Notably, the total energy transmission, which quantifies the energy flux from one CFT through the junction, is bounded above by the effective central charge associated with both the CFTs and the junction. Results for energy transport in conformal interfaces are recovered in a special limit. Furthermore, we extend our analysis to junctions connecting $N$ 2D CFTs.

Figures (6)

• Figure 1: Cartoon plot for ICFT$_2$ ( left) and ICFT$_N$ ( right) at a constant time slice. The red dot is the location of defect and each CFT is defined on a half-line.
• Figure 2: Cartoon plot for ICFT$_3$ at a constant time slice ( left) and with time direction added ( right). The red dot marks the defect location at $x_A=0$ and each CFT defined on the half-line $x_\text{A}<0,$ where $\text{A}=1,2,3$ .
• Figure 3: The plot for CFT$_A$ and its bulk dual geometry $N_\text{A}$. The junction brane $Q$ is shown in blue. The AdS boundary is at $u_\text{A}\to 0$. The entire system is formed by gluing $N$ such subsystems via maps that satisfy specific gluing conditions.
• Figure 4: The plots of tension $T$ as a function of $L_a$ with different AdS radii $L_1=1,L_2=2,L_3=4$ ( top-left), $L_1= L_2=1,L_3=3$ ( top-right), $L_1=1,L_2=L_3=3$ ( bottom-left) $L_1=2,L_2=L_3=3$ ( bottom-right). The red lines indicate the tension ranges specified in \ref{['eq:tensionran1']} and \ref{['eq:tensionran2']}, which are considered for energy transport calculations.
• Figure 5: Plots of junction entropy $\log g$ ( left) and energy reflection coefficients ( right) including $\mathcal{R}_1$ ( black), $\mathcal{R}_2$ ( blue), $\mathcal{R}_3$ ( red), as functions of tension $T$ for $L_1=1,L_2=2,L_3=4$.