On complexity growth in massive gravity theories, the effects of chirality and more

TL;DR

This paper investigates how parity-violation and chirality influence the rate of complexity growth in massive gravity theories using the Complexity=Action conjecture, revealing that increased chirality correlates with faster complexity growth.

Contribution

It provides the first analysis of complexity growth rates in chiral and parity-preserving massive gravity theories, highlighting the impact of chirality on complexity dynamics.

Findings

Decreasing the parameter μ increases complexity growth rate.

Complexity growth correlates more strongly with temperature than entropy.

Chirality enhances the rate of complexity growth in massive gravity solutions.

Abstract

To study the effect of parity-violation on the rate of complexity growth, by using "Complexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter $\mu$, which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped CFTs in the Tensor Network Renormalization picture.