Abstract
For an ordinary charged system, it has been shown that by using the "complexity equals action" (CA) conjecture, the late-time growth rate of the holographic complexity is given by a difference between the value of $\Phi_H Q+\Omega_H J$ on the inner and outer horizons. In this paper, we study the influence of the chiral anomaly on the complexity of the boundary quantum system. To be specific, we evaluate the CA holographic complexity of the charged supersymmetric black holes whose bulk action is modified by an additional Chern-Simons term of the electromagnetic fields. As a result, the late-time growth rate of the complexity will be corrected by some additional terms on the inner and outer horizons than the ordinary charged black holes. Our work implies that the late-time growth rate of the complexity can carry the information of the chiral anomaly for the boundary system.
Highlights
In recent years, there has been a growing interest in the idea that applies the quantum information theory into the gravitational theory in the context of the anti–de Sitter (AdS)=CFT correspondence
We evaluate the complexity equals action holographic complexity of the charged supersymmetric black holes whose bulk action is modified by an additional Chern-Simons term of the electromagnetic fields
We considered the five-dimensional minimal gauged supergravity, which is a special case of the Einstein-Maxwell-Chern-Simons theory
Summary
There has been a growing interest in the idea that applies the quantum information theory into the gravitational theory in the context of the AdS=CFT correspondence. The quantum circuit complexity of the boundary quantum system, which is defined by the minimal number of elementary gates required to construct a target state for a referent state, has been proposed to describe the information inside the black hole horizon [1,2]. We only consider the CA conjecture, which claims that the circuit complexity of the quantum state jψðtL; tRÞi in the boundary system is given by the onshell bulk gravitational action IWDW within the WheelerDeWitt (WDW) patch, which is enclosed by the past and future light sheets sent into the bulk spacetime from the time slices tL and tR, i.e., we have. To study the complexity of the boundary chiral system from the viewpoint of holography, we need a black hole solution in the Einstein-MaxwellChern-Simons theory.
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