Anomalous dimensions of higher spin currents in large N CFTs

Abstract

Abstract:We examine anomalous dimensions of higher spin currents in the critical O(N ) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories, respectively. We reproduce the known results on the anomalous dimensions to the leading order in 1/N by using conformal perturbation theory. This work can be regarded as an extension of previous work on the critical O(N ) scalars in 3 dimensions, where it was shown that the bulk computation for the masses of higher spin fields on AdS 4 can be mapped to the boundary one in conformal perturbation theory. The anomalous dimensions of the both theories agree with each other up to an overall factor depending only on d, and we discuss the coincidence for d = 3 by utilizing N = 2 supersymmetry.

Fermions in geodesic Witten diagrams

“…Thus, the spinor structure of the independent even dimensional GWD is probably different from the odd dimensional one. Interesting research topics in the odd dimensional CFT with fermion are, for example, 3d (supersymmetric) U (N ) model [29,[42][43][44] and 1d cSYK [45,46]. Make geodesic Witten diagram super One of the motivation of our work was to extend the arguments to the superconformal field theories (SCFT).…”

“…In these cases, we need to take the bulk-boundary propagators with relatively opposite chirality projection because of Γ A in (43) and (44). In appendix B.2, we leave intermediate steps from the derivative interaction (43) to the second spinor bi-linear in (42).…”

Correlators in higher-spin AdS3 holography from Wilson lines with loop corrections

“…The paper deals with loop corrections in two point Witten diagrams for higher spin theories on AdS d . Related previous works may be found in[3][4][5][6][7][8][9][10].…”

On the higher spin spectrum of Chern-Simons theory coupled to fermions in the large flavour limit

“…Theoretically, this theory is of interest because it is an example of a conformal field theory in d > 2 for which explicit expressions for the scaling dimensions of higher-spin operators can be calculated at strong coupling, similar to vector models such as the critical O(N ) model, or the Gross-Neveu model in higher dimensions. (See [5] for a review, and e.g., [6][7][8][9][10][11][12][13][14][15] for calculations of scaling dimensions in vector models related to this paper) or the large flavour limit of 3d QED and QCD (e.g., [16][17][18][19][20][21]). With the revival (e.g., [22][23][24]) of the bootstrap program [25], various interesting methods, results and theorems about higher spin operators, e.g., [26][27][28][29][30][31][32][33] have been developed recently, and comparison to expectations from these analyses is another motivation for this work.…”