Higher spin currents in the critical $O(N)$ vector model at $1/N^2$

Abstract

We calculate the anomalous dimensions of higher spin singlet currents in the critical $O(N)$ vector model at order $1/N^2$. The results are shown to be in agreement with the four-loop perturbative computation in ${\varphi }^4$ theory in $4-2\epsilon$ dimensions. It is known that the order $1/N$ anomalous dimensions of higher-spin currents happen to be the same in the Gross-Neveu and the critical vector model. On the contrary, the order $1/N^2$ corrections are different. The results can also be interpreted as a prediction for the two-loop computation in the dual higher-spin gravity.

17 pages, 5 figures; a sign typo fixed

References in corpus (3)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Anomalous dimensions of high-spin operators beyond the leading order
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization

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