Abstract
In this paper, we use the “complexity equals action” (CA) conjecture to explore the switchback effect in the strongly-coupled quantum field theories with finite N and finite coupling effects. In the perspective of holography, this is equivalent to evaluating the CA complexity in a Vaidya geometry equipped with a light shockwave for a higher curvature gravitational theory. Based on the Noether charge formalism of Iyer and Wald, we obtain the slope of the complexity of formation in the small- and large-time approximations. By circuit analogy, we show that our results concur with the switchback effect of the quantum system. These results show that the switchback effect is a general feature of the CA complexity in stationary black holes and its existence is independent of the explicit gravitational theory as well as spacetime background. From the viewpoint of AdS/CFT, this also implies that the switchback effect is a general feature of the thermofield double state in the strongly-coupled quantum field systems with finite N and finite coupling effects. Moreover, we also illustrate that unlike the late-time complexity growth rate, the counterterm plays an important role in the study of the switchback effect.
Highlights
In recent years, quantum information perspectives have provided many useful techniques for studying the AdS/CFT correspondence
The complexity equals action” (CA) conjecture states that the complexity of boundary state is given by evaluating the full onshell action of the bulk gravitational theory on the Wheeler– DeWitt (WDW) patch, which is the causal development of a spacelike bulk surface (Cauchy surface) connected the boundary timeslices tL and tR, i.e., CA (|ψ(tL, tR)
We use the CA conjecture to investigate the switchback effect of the thermofield double (TFD) state following a quantum quench in the strongly-coupled quantum system with finite N and finite coupling effects
Summary
Quantum information perspectives have provided many useful techniques for studying the AdS/CFT correspondence. The holographic dual of this process is given by the Vaidya geometry, which is equipped with a thin shell of null fluid collapse (shockwave) [82,83,84,85,86,87,88,89] Based on this duality, the time dependence of the complexity in the boundary quantum field system has been studied by using different holographic complexities [40,65,66,67,68,69,70,71].
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