On decoding the string from interfaces in 2d conformal field theories

TL;DR

This paper explores the holographic duality between gravitational junctions in 3D anti-de Sitter space and interface phenomena in conformal field theories, revealing how string solutions encode boundary wave-packets and entanglement properties.

Contribution

It establishes a detailed correspondence between Nambu-Goto string solutions and interface states in CFTs, including wave-packet reflection and entanglement entropy insights.

Findings

Wave-packets are perfectly reflected at the interface without shape distortion.

Entanglement entropy reveals stringy modes even in the tensionless limit.

Strong sub-additivity of entanglement entropy is satisfied and saturated for symmetric intervals.

Abstract

General solutions of a gravitational junction between two copies of a three-dimensional Einstein manifold $\mathcal{M}$ correspond to the solutions of the non-linear Nambu-Goto equation for a string in $\mathcal{M}$. We show that, for the junctions in three-dimensional anti-de Sitter spacetimes constituted by tensile strings, which are dual to interfaces between thermal states in conformal field theories, the solutions of the Nambu-Goto equation describing the junction correspond to state-dependent wave-packets, which are perfectly reflected at the interface to future null infinity without shape distortion when incident from past null infinity. These wavepackets are realized by state-dependent half-sided conformal transformations and affect the expectation value of the displacement operator. We further show that the entanglement entropy of an interval straddling the interface deciphers the stringy modes of the dual junction even in the tensionless limit. We also demonstrate that the strong sub-additivity of entanglement entropy is satisfied and is saturated for symmetric intervals generally.