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

Abstract

To study the effect of parity-violation on the rate of complexity growth, by using "Com-plexity=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 µ, 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.

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

“…The warped AdS would have deformed constructions depending on the value of ν. These plots show the respective relations between these three manifolds again shows that the "complexity=action" could be used for the WAdS/WCFT case [24,30].…”

“…Along the way, we use many known results for the partition function, properties of the dual holographic gravitational theories such as chiral Liouville action, the proposed actions for WCFTs such as those found in [22], the anomaly behaviors, and the structure of entanglement entropy and holographic complexity of warped CFTs derived in previous works [24,37]. It worths to mention here that in fact there are various examples in real world for these field theories, such as the continuum limit of large N chiral Potts model [31,38] which is a spin model on a planar lattice.…”

“…In fact, in our previous work [24] we proposed the following connections, 16) or one can also write this action in the following form…”

“…In the NMG action, the mass of graviton plays the essential role which affects various quantum information quantities of the model, such as entanglement and its evolutions during quench processes, entanglement and complexity of purification, etc, which were studied in more details in [24,37,62,63].…”

“…Also, in this setup, it has been shown that the entropy of a thermal state matches with the entropy of a warped BTZ black hole. In addition, the calculations for entanglement entropy and even subregion complexity have already been done for such solutions [24][25][26]. Furthermore, interesting relationships between WCFTs which show semi-local properties and other models such as SYK with complex fermions which has maximal chaos have been found in [27].…”