Nonuniqueness of Green's functions at special points

We investigate a new property of retarded Green's functions using AdS/CFT. The Green's functions are not unique at special points in complex momentum space. This arises because there is no unique incoming mode at the horizon and is similar to the "pole-skipping" phenomenon in holographic chaos. Our examples include the bulk scalar field, the bulk Maxwell vector and scalar modes, and the shear mode of gravitational perturbations. In these examples, the special points are always located at $ω_\star = -i(2πT)$ with appropriate values of complex wave number.

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