Semiclassical spectrum of the Ising CFT

Abstract

We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $\lambda {\varphi }^4$ theory in $d=4-\epsilon$, we obtain the full spectrum of composite operators built out of $n$ fields transforming according to the various Lorentz representations to next-to-leading order in the double--scaling limit $n\to \infty$ and $\lambda \to 0$ with $\lambda n$ fixed. At any given order, the semiclassical expansion resums an infinite number of Feynman diagrams. Combining our results with existing perturbative computations further yields the complete five-loop scaling dimensions in the $\epsilon$-expansion for the family of ${\varphi }^n$ operators. Finally, extrapolating the semiclassical results to three dimensions leads to a competitive alternative to existing methodologies.

6 pages, 3 figures, 1 table. v2: Presentation revised to match the published version