Holographic Complexity in a Charged Supersymmetric Black Holes

TL;DR

This paper investigates how the chiral anomaly affects the holographic complexity growth rate in charged supersymmetric black holes using the CA conjecture, revealing additional horizon contributions due to Chern-Simons modifications.

Contribution

It introduces the impact of chiral anomaly via Chern-Simons terms on the complexity growth rate in supersymmetric black holes, extending the CA conjecture analysis.

Findings

Complexity growth rate is corrected by additional horizon terms.

Chiral anomaly influences the late-time complexity growth.

The work links boundary anomalies to bulk complexity dynamics.

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.