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  • Letter
  • Open Access

Krylov complexity in conformal field theory

Anatoly Dymarsky1,2 and Michael Smolkin3

  • 1Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
  • 2Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Moscow 143026, Russia
  • 3The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

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Phys. Rev. D 104, L081702 – Published 1 October, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L081702

Abstract

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.

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Outline

Information

Phys. Rev. D 104, L081702– Published 1 October, 2021
  • Received 17 June 2021
  • Accepted 7 September 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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