Investigating the holographic complexity in Einsteinian cubic gravity

In this paper, we investigate the holographic complexity of a small mass AdS black hole in Einsteinian cubic gravity by using the “complexity equals action” (CA) and “complexity equals volume” (CV) conjectures. In the CA context, the late-time growth rate satisfies the Lloyd bound for the $$k=0$$ and $$k=1$$ cases but it violates it for the $$k=-1$$ case in the first-order approximation of the small mass parameter. However, by a full-time analysis, we find that this late-time limit is approached from above, which implies that this bound in all of these cases will be violated. In the CV context, we considered both the original and the generalized CV conjectures. Differing from the CA conjecture, the late-time rate here is non-vanishing in the zeroth-order approximation, and this shows that the Lloyd bound is exactly violated even in the late-time limit. These results show numerous differences from the neutral case of the Einstein gravity in both the CA and the CV holographic contexts where all of their late-time results saturate the Lloyd bound. These differences illustrate the influence of the higher curvature correction in Einstein gravity