What kind of “complexity” is dual to holographic complexity?

Abstract It is assumed that the holographic complexities such as complexity-action (CA) and complexity-volume (CV) conjecture are dual to complexity in field theory. However, because definition of theory still not complete, confirmation duality ambiguous. To improve this situation, we approach problem from a different angle. We first identify minimal genuin properties filed should satisfy without assuming anything circuit or information Based on these properties, propose formula complexity. Our implies between certain states two dimensional CFTs given by Liouville action, which compatible with path-integral gives natural interpretations for both CA CV conjectures what their reference are. When applied thermo-field double states, it also consistent results conjecture: divergent term finite term.