The gravity dual of real-time CFT at finite temperature

BOTTA-CANTCHEFF, MARCELO; MARTÍNEZ, PEDRO J.; SILVA, GUILLERMO A.

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

SPRINGER

Año: 2018 vol. 2018

1029-8479

We present a spherically symmetric aAdS gravity solution with SchwingerKeldysh 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 piecesare interpreted as the gravity duals of the two Euclidean β/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. In this framework, we compute the time ordered 2-pt functions of scalar CFT operators via a non-back-reacting Klein-Gordon field for both backgrounds and confront the results. When solving for the field we find that the gluing leads to a geometric realization of the Unruh trick via a completely holographic prescription.Interesting observations follow from hOLORi, which capture details of the entanglement of the (ground) state and the connectivity of the spacetime.