Holographic and QFT complexity with angular momentum

A bstract We study the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. Using holographic complexity=action (CA) and complexity=volume (CV) proposals, we full time dependence formation two dimensional BTZ. The obtained results their turn out be analogous those charged Reissner-Nordström AdS For CA, our computation carefully accounts counterterm in gravity action, which was not included previous analysis literature. This affects early its effect becomes negligible close extremality. In grand canonical ensemble, CA CV are linear temperature, diverge with same structure speed light velocity limit. inclusion is crucial both effects. also address problem studying higher holes, focusing four Kerr-AdS case. Carefully taking into account all ingredients, show that late limit growth rate saturates expected bound, find large holes diverges critical Our complemented by circuit a free scalar model thermofield double (TFD) state momentum. how this can given description terms non-rotating TFD introducing mode-by-mode effective temperatures times. comment similarities differences QFT results.