Abstract
We study the evolution of holographic subregion complexity under a thermal quench in this paper. From the subregion CV proposal in the AdS/CFT correspondence, the subregion complexity in the CFT is holographically captured by the volume of the codimension-one surface enclosed by the codimension-two extremal entanglement surface and the boundary subregion. Under a thermal quench, the dual gravitational configuration is described by a Vaidya-AdS spacetime. In this case we find that the holographic subregion complexity always increases at early time, and after reaching a maximum it decreases and gets to saturation. Moreover we notice that when the size of the strip is large enough and the quench is fast enough, in AdSd+1(d ≥ 3) spacetime the evolution of the complexity is discontinuous and there is a sudden drop due to the transition of the extremal entanglement surface. We discuss the effects of the quench speed, the strip size, the black hole mass and the spacetime dimension on the evolution of the subregion complexity in detail numerically.
Highlights
From the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence, there have been two different proposals on holographic complexity, which are referred to as the CV (Complexity=Volume) conjecture [1, 2, 17, 18] and the CA (Complexity=Action) conjecture [19, 20] respectively
We study the evolution of holographic subregion complexity under a thermal quench in this paper
The thermal quench in CFT could be described holographically by the dynamical Vaidya spacetime, whose initial state corresponds to the pure AdS and the final state corresponds to the SAdS black hole
Summary
We introduce the general framework to study the subregion complexity in the time-dependent background corresponding to a thermal-quenched CFT. A thermal quench in a CFT can be described holographically by the collapsing of a thin shell of null dust falling from the AdS boundary to form a black hole. This process can be modeled by a Vaidya-AdS metric. As proposed in [29], the subregion complexity in a static background is proportional to the volume of a codimension-one time slice in the bulk geometry enclosed by the boundary region and the corresponding extremal codimension-two Ryu-Takayanagi (RT) surface. To get the corresponding subregion complexity, we need work out the corresponding extremal codimension-two surface γA first
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