Regular Article - Theoretical Physics
What kind of “complexity” is dual to holographic complexity?
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Yaguan Road 135, Jinnan District, 300350, Tianjin, People’s Republic of China
2 Institute of Theoretical Physics, Chinese Academy of Science, 100190, Beijing, People’s Republic of China
3 School of Physical Science, University of Chinese Academy of Science, 100049, Beijing, People’s Republic of China
4 Department of Physics and Siyuan Laboratory, Jinan University, 510632, Guangzhou, People’s Republic of China
5 Department of Physics and Photon Science, Gwangju Institute of Science and Technology, 123 Cheomdan-gwagiro, 61005, Gwangju, Korea
6 Research Center for Photon Science Technology, Gwangju Institute of Science and Technology, 123 Cheomdan-gwagiro, 61005, Gwangju, Korea
Accepted: 19 February 2022
Published online: 26 March 2022
It is assumed that the holographic complexities such as the complexity-action (CA) and the complexity-volume (CV) conjecture are dual to complexity in field theory. However, because the definition of the complexity in field theory is still not complete, the confirmation of the holographic duality of the complexity is ambiguous. To improve this situation, we approach the problem from a different angle. We first identify minimal and genuin properties that the filed theory dual of the holographic complexity should satisfy without assuming anything from the circuit complexity or the information theory. Based on these properties, we propose a field theory formula dual to the holographic complexity. Our field theory formula implies that the complexity between certain states in two dimensional CFTs is given by the Liouville action, which is compatible with the path-integral complexity. It gives natural interpretations for both the CA and CV conjectures and identify what their reference states are. When applied to the thermo-field double states, it also gives consistent results with the holographic results in the CA conjecture: both the divergent term and finite term.
© The Author(s) 2022
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