Decoding the string in terms of holographic quantum maps

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 at the level of linearized gravitational perturbations that each stringy mode of the junction corresponds to a $\mathcal{H}_{in}\rightarrow \mathcal{H}_{out}$ quantum map which can be factorized into a scattering matrix involving reflection/transmission and a relative automorphism of the Virasoro algebra, and also a $\mathcal{H}_{L}\rightarrow \mathcal{H}_{R}$ map of similar nature. These maps preserve the conformal boundary condition, are independent of the background conformal frame, as in the case of conformal interfaces studied in the literature, and realize a tunable energy transmitter.