Krylov Complexity in Quantum Field Theory

Nuclear Physics B, vol. 993, pp. 116263

Abstract

In this paper, we study the Krylov complexity in quantum field theory and make a connection with the holographic “Complexity equals Volume” conjecture. When Krylov basis matches with Fock basis, for several interesting settings, we observe that the Krylov complexity equals the average particle number showing that complexity scales with volume. Using similar formalism, we compute the Krylov complexity for free scalar field theory and find surprising similarities with holography. We also extend this framework for field theory where an inverted oscillator appears naturally and explore its chaotic behavior.

Authors 3

1. Kiran Adhikari Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, D-52056, Aachen, Germany

2. Sayantan Choudhury corresponding

   Tata Institute of Fundamental Research · Shree Guru Gobind Singh Tricentenary University · International Centre for Theoretical Sciences

   Affiliation as printed

   Centre For Cosmology and Science Popularization (CCSP), SGT University, Gurugram, Delhi- NCR, Haryana- 122505, India

   International Centre for Theoretical Sciences, Tata Institute of Fundamental Research (ICTS-TIFR), Shivakote, Bengaluru 560089, India

3. Abhishek Roy

   Indian Institute of Technology Jodhpur

   Affiliation as printed

   Department of Physics, Indian Institute of Technology Jodhpur, Karwar, Jodhpur 342037, India