Content area
Abstract
We compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the “complexity-action” (CA) conjecture and “complexity-volume” (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is 2E/(πℏ) saturating the Lloyd’s bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.
Details
1 Quantum Universe Center, Korea Institute for Advanced Study, Seoul, South Korea
2 School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju, South Korea
3 Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China; Center for High Energy Physics, Peking University, Beijing, China