The holographic dual of an EPR pair has a wormhole

Abstract

We construct the holographic dual of two colored quasiparticles in maximally supersymmetric Yang-Mills theory entangled in a color singlet EPR pair. In the holographic dual the entanglement is encoded in a geometry of a non-traversable wormhole on the worldsheet of the flux tube connecting the pair. This gives a simple example supporting the recent claim by Maldacena and Susskind that EPR pairs and non-traversable wormholes are equivalent descriptions of the same physics.

Figures (4)

• Figure 1: The Penrose diagram of an eternal AdS black hole.
• Figure 2: The holographic $q$-$\bar{q}$ system entangled into a color-neutral EPR pair.
• Figure 3: The casual structure on the string worldsheet. The thick red lines indicate the worldlines of the quark and anti-quark, and the string worldsheet fills the universe in between. The solid lines indicate the worldsheet horizons, which happens to be the location of the Rindler horizons for each of the quarks. The solid dots denote events where light rays are emitted from the quark and anti-quark into the dual worldsheet, and the dotted lines indicate the resulting lightlike trajectories. The string worldsheet clearly has the same causal structure of an eternal AdS black hole as in Figure \ref{['F:penrose']}.
• Figure 4: Entanglement entropy for field theory on a circle, with ends identified. By tracing over the degrees of freedom in the causal development of B (the shaded region) we obtain a reduced density matrix on A which completely specifies the state of the system within its causal development.