Abstract
We study the pole-skipping phenomenon of the scalar retarded Green's function in the rotating BTZ black hole background. In the static case, the pole-skipping points are typically located at negative imaginary Matsubara frequencies $\omega=-(2\pi T)ni$ with appropriate values of complex wave number $q$. But, in a $(1+1)$-dimensional CFT, one can introduce temperatures for left-moving and right-moving sectors independently. As a result, the pole-skipping points $\omega$ depend both on left and right temperatures in the rotating background. In the extreme limit, the pole-skipping does not occur in general. But in a special case, the pole-skipping does occur even in the extreme limit, and the pole-skipping points are given by right Matsubara frequencies.
Highlights
AND SUMMARYThe AdS=CFT duality or holography [1–4] is a useful tool to study strongly coupled systems
We study the pole skipping phenomenon of the scalar retarded Green’s function in the rotating BTZ black hole background
The pole skipping was originally discussed in the context of holographic chaos [13–17]
Summary
The AdS=CFT duality or holography [1–4] is a useful tool to study strongly coupled systems (see, e.g., Refs. [5–9]). For the BTZ black hole, analytic Green’s function can be derived both for the nonextreme case and for the extreme case, so one can study the pole skipping in the extreme limit, and there is no pole skipping in general (Point 2). There is an exceptional case, and the pole skipping does occur even in the extreme limit (Point 3) This occurs when ν 1⁄4 1, and the pole skipping points ω are given by right Matsubara frequencies. In the extreme limit TL → 0, the left contribution gives only a power-law behavior ðω − qÞν in the Green’s function (with possible log terms when there is matter conformal anomaly), and there is no nontrivial poles nor zeros. In the extreme limit, one still has the nonvanishing right temperature TR, so the pole skipping is possible
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