Energy Reflection and Transmission at 2D Holographic Interfaces

Scattering from conformal interfaces in two dimensions is universal in that the flux of reflected and transmitted energy does not depend on the details of the initial state. In this Letter, we present the first gravitational calculation of energy reflection and transmission coefficients for interfaces with thin-brane holographic duals. Our result for the reflection coefficient depends monotonically on the tension of the dual string anchored at the interface and obeys the lower bound recently derived from the averaged-null-energy condition in conformal field theory. The boundary-conformal-field-theory limit is recovered for infinite ratio of the central charges.

Figure 1

Illustration of the holographic-interface geometry. The two spacetimes are glued together at the location of the world sheet $Q_L\equiv Q_R$. The interface $P$ is the intersection of the world sheet with the conformal boundary. The incident wave is denoted by $I$, and the reflected and transmitted waves are denoted by $R$ and $T$.