# Modified "complexity equals action" conjecture

## TL;DR

This paper modifies the 'complexity equals action' conjecture to address divergence issues in certain gravity theories, proposing a new boundary action-based measure that aligns with circuit analysis and tests it via Vaidya geometry.

## Contribution

The paper introduces a modified CA conjecture that avoids divergence problems and better matches circuit model predictions in holographic complexity.

## Key findings

- Modified conjecture yields finite complexity growth rates.
- Late time growth rate equals entropy times temperature.
- Switchback effect is confirmed in Vaidya geometry.

## Abstract

In this paper, we first use the "complexity equals action" conjecture to discuss the complexity growth rate in both perturbation Einsteinian cubic gravity and non-perturbation Einstein-Weyl gravity. We find that the CA complexity rate in these cases is divergent. To avoid this divergence, we modify the original conjecture, where we assume that the complexity of the boundary state equals the boundary actions contributed by the null segments as well as the joints of the Wheeler-DeWitt patch. Then, the late time growth rate of this modified holographic complexity is given by entropy $S$ times temperature $T$, which is quite in agreement with the circuit analysis. Finally, to test its rationality, we also investigate the switchback effect by evaluating it in a Vaidya geometry and analyze the results in circuit models.