Comparison of holographic and field theoretic complexities for time dependent thermofield double states

• Published in: The journal of high energy physics Vol. 2018; no. 2; pp. 1 - 40
• Main Authors: Yang, Run-Qiu, Niu, Chao, Zhang, Cheng-Yong, Kim, Keun-Young
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Complexity; Elementary Particles; Gauge-gravity correspondence; High energy physics; Holography and condensed matter physics (AdS/CMT); Physics; Physics and Astronomy; Proposals; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Time dependence; Gauge-gravity correspondence; Holography and condensed matter physics (AdS/CMT)
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2018)082

A bstract 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 2 E/ (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.