Comments on the double cone wormhole

Understand

In this paper we revisit the double cone wormhole introduced by Saad, Shenker and Stanford (SSS), which was shown to reproduce the ramp in the spectral form factor.

• As a first approximation we can say that this solution computes $\textrm{Tr}[e^{-iKT}]$, a trace of the "evolution" operator that generates Schwarzschild time translations on the two sided wormhole geometry.
• This point of view leads to a simple way to compute the normalization factor of the wormhole.
• When we have bulk matter fields, SSS suggested using a modified evolution $\tilde K$ which involves a slightly complex geometry, so that we are really computing $\textrm{Tr}[e^{-i\tilde{K}T}]$.