Holographic complexity equals which action?

• Main Authors: Kanato Goto, Hugo Marrochio, Robert C. Myers, Leonel Queimada, Beni Yoshida
• Format: Article
• Language: English
• Published: SpringerOpen 2019-02-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Black Holes; Black Holes in String Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP02(2019)160

Abstract We revisit the complexity = action proposal for charged black holes. We investigate the complexity for a dyonic black hole, and we find the surprising feature that the late-time growth is sensitive to the ratio between electric and magnetic charges. In particular, the late-time growth rate vanishes when the black hole carries only a magnetic charge. If the dyonic black hole is perturbed by a light shock wave, a similar feature appears for the switchback effect, e.g. it is absent for purely magnetic black holes. We then show how the inclusion of a surface term to the action can put the electric and magnetic charges on an equal footing, or more generally change the value of the late-time growt rate. Next, we investigate how the causal structure influences the late-time growth with and without the surface term for charged black holes in a family of Einstein-Maxwell-Dilaton theories. Finally, we connect the previous discussion to the complexity=action proposal for the two-dimensional Jackiw-Teitelboim theory. Since the two-dimensional theory is obtained by a dimensional reduction from Einstein-Maxwell theory in higher dimensions in a near-extremal and near-horizon limit, the choices of parent action and parent background solution determine the behaviour of holographic complexity in two dimensions.