In the AdS3 Vaidya geometry, the extremal volume defining holographic subregion complexity is genuinely x-dependent during the quench, so the standard x-independent ansatz fails at intermediate times; early and late time approximations are derived.
Divergences in the rate of complexification
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abstract
It is conjectured that the average energy provides an upper bound on the rate at which the complexity of a holographic boundary state grows. In this paper, we perturb a holographic CFT by a relevant operator with a time-dependent coupling, and study the complexity of the time-dependent state using the \textit{complexity equals action} and the \textit{complexity equals volume} conjectures. We find that the rate of complexification according to both of these conjectures has UV divergences, whereas the instantaneous energy is UV finite. This implies that neither the \textit{complexity equals action} nor \textit{complexity equals volume} conjecture is consistent with the conjectured bound on the rate of complexification.
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On volume subregion complexity in Vaidya spacetime
In the AdS3 Vaidya geometry, the extremal volume defining holographic subregion complexity is genuinely x-dependent during the quench, so the standard x-independent ansatz fails at intermediate times; early and late time approximations are derived.