TY - JOUR

T1 - On CJ and CT in the Gross-Neveu and O(N) models

AU - Diab, Kenan

AU - Fei, Lin

AU - Giombi, Simone

AU - Klebanov, Igor R.

AU - Tarnopolsky, Grigory

N1 - Funding Information:
We thank Z Komargodski, F Kos, H Osborn, A Petkou, S Pufu, K Sen and A Stergiou for useful discussions and communications. The work of SG was supported in part by the US NSF under Grant No.?PHY-1318681. The work of IRK and GT was supported in part by the US NSF under Grant No.?PHY-1314198. The work of KD was supported in part by the US NSF Graduate Research Fellowship under Grant No. DGE 1148900.
Publisher Copyright:
© 2016 IOP Publishing Ltd.

PY - 2016/9/14

Y1 - 2016/9/14

N2 - 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.

AB - 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.

KW - conformal field theory

KW - large N expansion

KW - renormalization group

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U2 - 10.1088/1751-8113/49/40/405402

DO - 10.1088/1751-8113/49/40/405402

M3 - Article

AN - SCOPUS:84988928082

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 40

M1 - 405402

ER -