Path-integral complexity for perturbed CFTs

Arpan Bhattacharyya, Pawel Caputa, Sumit R. Das, Nilay Kundu, Masamichi Miyaji, Tadashi Takayanagi

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


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.

Original languageEnglish
Article number86
JournalJournal of High Energy Physics
Issue number7
StatePublished - Jul 1 2018

Bibliographical note

Funding Information:
Article funded by SCOAP3.

Publisher Copyright:
© 2018, The Author(s).


  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Renormalization Group

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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