2017/10/02 by Keunyoung Kim, Keun-Young Kim, Chao Niu +6 · 27 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Cosmology and Gravitation Theories #FOS: Physical sciences #Field (mathematics) #Finsler manifold #General Relativity and Quantum Cosmology (gr-qc) #Geometry #High Energy Physics - Theory (hep-th) #Holography #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Physics (quant-ph) #Quantum mechanics #Scalar curvature #Theoretical physics #Upper and lower bounds #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1710.00600
published in arXiv (Cornell University) (Cornell University) · Changed the title, modified some figures, revised some typos, added references and appendix
openalex publication_date 2017/10/02 · arxiv created 2017/11/09 · arxiv updated 2017/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.