Skip to main content

On C-J and C-T in the Gross-Neveu and O(N) models

Author(s): Diab, Kenan S; Fei, Lin; Giombi, Simone; Klebanov, Igor R; Tarnopolsky, Grigory

To refer to this page use:
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 - epsilon 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 2 + epsilon dimensions and the Gross-Neveu-Yukawa model in 4 - epsilon dimensions. For small values of N, we use Pade approximants based on the 4 - epsilon and 2 + epsilon 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 C-T(UV) > C-T(IR) applies both to the GN and the scalar O(N) models in d = 3.
Publication Date: 7-Oct-2016
Electronic Publication Date: 14-Sep-2016
Citation: Diab, Kenan, Fei, Lin, Giombi, Simone, Klebanov, Igor R, Tarnopolsky, Grigory. (2016). On C-J and C-T in the Gross- Neveu and O(N) models. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 49 (10.1088/1751-8113/49/40/405402
DOI: doi:10.1088/1751-8113/49/40/405402
ISSN: 1751-8113
EISSN: 1751-8121
Type of Material: Journal Article
Version: Author's manuscript

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.