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Path-integral complexity for perturbed CFTs

  • Arpan Bhattacharyya
  • Pawel Caputa
  • Sumit R. Das
  • Nilay Kundu
  • Masamichi Miyaji
  • Tadashi Takayanagi
Open Access
Regular Article - Theoretical Physics

Abstract

In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories. Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings. Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence. Last but not the least, we estimate contributions to complexity from relevant perturbations.

Keywords

AdS-CFT Correspondence Renormalization Group Conformal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Arpan Bhattacharyya
    • 1
  • Pawel Caputa
    • 1
  • Sumit R. Das
    • 2
  • Nilay Kundu
    • 1
  • Masamichi Miyaji
    • 1
  • Tadashi Takayanagi
    • 1
    • 3
  1. 1.Center for Gravitational Physics, Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  2. 2.Department of Physics and AstronomyUniversity of KentuckyLexingtonU.S.A.
  3. 3.Kavli Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwaJapan

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