Abstract
Recently, it is shown that many Green's functions are not unique at special points in complex momentum space using AdS/CFT. This phenomenon is similar to the pole-skipping in holographic chaos, and the special points are typically located at $\omega_n = -(2\pi T)ni$ with appropriate values of complex wave number $q_n$. We study finite-coupling corrections to special points. As examples, we consider four-derivative corrections to gravitational perturbations and four-dimensional Maxwell perturbations. While $\omega_n$ is uncorrected, $q_n$ is corrected at finite coupling. Some special points disappear at particular values of higher-derivative couplings. Special point locations of the Maxwell scalar and vector modes are related to each other by the electromagnetic duality.
Highlights
The AdS=CFT duality or holography [1,2,3,4] is a useful tool to study strongly coupled systems
In addition to the gravitational sound mode which was originally discussed in holographic chaos, the bulk scalar field, the bulk Maxwell field, the gravitational
We study the corrections to the first few special points and their implications
Summary
The AdS=CFT duality or holography [1,2,3,4] is a useful tool to study strongly coupled systems (see, e.g., Refs. [5,6,7,8,9]). A number of papers have appeared which study a new aspect of retarded Green’s functions using AdS=CFT [10,11,12] According to these works, many Green’s functions are not unique at “special points” in complex momentum space (ω; q), where ω is frequency and q is wave number. Higher-derivative corrections to the special point have been discussed in Ref. Higher-derivative corrections to special points have been studied to some extent for the sound mode but have not been explored for the other perturbations which exhibit the pole skipping. We study higher-derivative corrections to these “nonchaotic” special points. The duality has an interesting consequence to the pole skipping: special point locations of the Maxwell scalar and vector modes are related to each other (Sec. IV C).
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