### Abstract

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 language | English (US) |
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Article number | 405402 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 40 |

DOIs | |

State | Published - Sep 14 2016 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Keywords

- conformal field theory
- large N expansion
- renormalization group

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## Cite this

_{J}and C

_{T}in the Gross-Neveu and O(N) models.

*Journal of Physics A: Mathematical and Theoretical*,

*49*(40), [405402]. https://doi.org/10.1088/1751-8113/49/40/405402