On the large charge sector in the critical O(N) model at large N

Simone Giombi, Jonah Hyman

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We study operators in the rank-j totally symmetric representation of O(N) in the critical O(N) model in arbitrary dimension d, in the limit of large N and large charge j with j/N ≡ ĵ fixed. The scaling dimensions of the operators in this limit may be obtained by a semiclassical saddle point calculation. Using the standard Hubbard-Stratonovich description of the critical O(N) model at large N, we solve the relevant saddle point equation and determine the scaling dimensions as a function of d and ĵ , finding agreement with all existing results in various limits. In 4 < d < 6, we observe that the scaling dimension of the large charge operators becomes complex above a critical value of the ratio j/N, signaling an instability of the theory in that range of d. Finally, we also derive results for the correlation functions involving two “heavy” and one or two “light” operators. In particular, we determine the form of the “heavy-heavy-light” OPE coefficients as a function of the charges and d.

Original languageEnglish (US)
Article number184
JournalJournal of High Energy Physics
Issue number9
StatePublished - Sep 2021

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • 1/N Expansion
  • Conformal Field Theory
  • Field Theories in Higher Dimensions
  • Global Symmetries


Dive into the research topics of 'On the large charge sector in the critical O(N) model at large N'. Together they form a unique fingerprint.

Cite this