Holographic Complexity in a Charged Supersymmetric Black Holes

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.

8 pages, 3 figures, and this paper has been accepted by PRD

References in corpus (8)

• Complexity and Shock Wave Geometries
• Gravitational action with null boundaries
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On Volumes of Subregions in Holography and Complexity
• Holographic Complexity Equals Which Action?
• Complexity in de Sitter Space
• Complexity for Charged Thermofield Double States
• Investigating two counting methods of the holographic complexity

Cited by in corpus (2)

• Action complexity of charged black holes with higher derivative interactions
• Holographic complexity of rotating black holes