The Gravity Dual of Real-Time CFT at Finite Temperature

Understand

We present a spherically symmetric aAdS gravity solution with Schwinger-Keldysh boundary condition dual to a CFT at finite temperature defined on a complex time contour.

• The geometry is built by gluing the exterior of a two-sided AdS Black Hole, the (aAdS) Einstein-Rosen wormhole, with two Euclidean black hole halves.
• These pieces are interpreted as the gravity duals of the two Euclidean $\beta/2$ segments in the SK path, each coinciding with a Hartle-Hawking-Maldacena (TFD) vacuum state, while the Lorentzian regions naturally describes the real-time evolution of the TFD doubled system.
• Within the context of Skenderis and van Rees real-time holographic prescription, the new solution should be compared to the Thermal AdS spacetime since both contribute to the gravitational path integral.