Reconstructing bulk equation of motion using CFT modular Hamiltonians

Nele Callebaut, Gilad Lifschytz

Research output: Contribution to journalArticlepeer-review


In the framework of bulk reconstruction, we elucidate the relationship between the action of CFT modular Hamiltonians on bulk operators, the possible equation of motion for the bulk operators, and the charge distribution at infinity corresponding to such bulk fields. In particular for scalar fields interacting with gravity or with gauge fields, we show how CFT considerations of the action of the modular Hamiltonian constrain the possible bulk equation of motion to be consistent with bulk gauge invariance and diffeomorphism invariance. In fact we show that requiring that the action of the modular Hamiltonian on a dressed bulk scalar operator be compatible with some unknown simple equation of motion, fixes, under reasonable assumptions, both the equation of motion and the action of the modular Hamiltonian once the first order 1N terms are known.

Original languageEnglish
Article number289
JournalJournal of High Energy Physics
Issue number8
StatePublished - Aug 2022


  • AdS-CFT Correspondence
  • Gauge Symmetry

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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