Decoding the string in terms of holographic quantum maps

TL;DR

The paper shows that the gravitational two-way junction in AdS$_3$, including its stringy degrees of freedom, can be decoded into universal quantum maps between the in/out Hilbert spaces of excitations at a conformal interface. The analysis connects the bulk Israel junction conditions to the Nambu-Goto equation for a worldsheet, with the stringy mode encoded by a normalizable NG mode, and derives the corresponding energy fluxes via holographic renormalization. A key result is that the interface implements universal maps that preserve the conformal boundary condition, yielding a tunable energy transmitter characterized by a universal transmission/reflection structure and an S-matrix that depends on a single parameter $\lambda$. The findings illuminate how stringy degrees of freedom of gravitational junctions manifest as quantum maps in the dual CFT, with potential implications for subregion reconstruction, energy conditions, and quantum information aspects of holographic interfaces.

Abstract

It has recently been shown that the Nambu-Goto equation for a string emerges from the junction conditions in three-dimensional gravity. Holographically, gravitational junctions are dual to interfaces in conformal field theory. We demonstrate that each stringy mode of the junction corresponds to a universal $\mathcal{H}_{in}\rightarrow \mathcal{H}_{out}$ quantum map between in and out Hilbert spaces of excitations scattered at the interface, and also a universal $\mathcal{H}_{L}\rightarrow \mathcal{H}_{R}$ quantum map relating the excitations on both sides. These quantum maps generalize those realized by defect operators, preserve the conformal boundary condition at the interface, and realize a tunable energy transmitter.

Figures (1)

• Figure 1: A two-way gravitational junction formed by gluing two AdS$_3$ manifolds by identifying points $P_{1,2}$ on the (gray) hypersurfaces. The incoming and outgoing plane wave amplitudes are indicated in the boundary CFT by arrows. The $a_n$ are classical string excitations.