On CJ and CT in the Gross-Neveu and O(N) models

Kenan Diab, Lin Fei, Simone Giombi, Igor R. Klebanov, Grigory Tarnopolsky

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We apply large N diagrammatic techniques for theories with double-trace interactions to the leading corrections to C J, the coefficient of a conserved current two-point function, and C T, the coefficient of the stress-energy tensor two-point function. We study in detail two famous conformal field theories in continuous dimensions, the scalar O(N) model and the Gross-Neveu (GN) model. For the O(N) model, where the answers for the leading large N corrections to C J and C T were derived long ago using analytic bootstrap, we show that the diagrammatic approach reproduces them correctly. We also carry out a new perturbative test of these results using the O(N) symmetric cubic scalar theory in 6 - dimensions. We go on to apply the diagrammatic method to the GN model, finding explicit formulae for the leading corrections to C J and C T as a function of dimension. We check these large N results using regular perturbation theory for the GN model in dimensions and the Gross-Neveu-Yukawa model in dimensions. For small values of N, we use Padé approximants based on the and expansions to estimate the values of C J and C T in d = 3. For the O(N) model our estimates are close to those found using the conformal bootstrap. For the GN model, our estimates suggest that, even when N is small, C T differs by no more than 2% from that in the theory of free fermions. We find that the inequality applies both to the GN and the scalar O(N) models in d =3.

Original languageEnglish (US)
Article number405402
JournalJournal of Physics A: Mathematical and Theoretical
Issue number40
StatePublished - Sep 14 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


  • conformal field theory
  • large N expansion
  • renormalization group


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