1. Exact Results for Scaling Dimensions of Composite Operators in the $\phi^4$ Theory
- Author
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Antipin, Oleg, Bersini, Jahmall, and Sannino, Francesco
- Subjects
High Energy Physics - Theory ,Condensed Matter - Statistical Mechanics ,High Energy Physics - Lattice ,High Energy Physics - Phenomenology - Abstract
We determine the scaling dimension $\Delta_n$ for the class of composite operators $\phi^n$ in the $\lambda \phi^4$ theory taking the double scaling limit $n\rightarrow \infty$ and $\lambda \rightarrow 0$ with fixed $\lambda n$ via a semiclassical approach. Our results resum the leading power of $n$ at any loop order. In the small $\lambda n$ regime we reproduce the known diagrammatic results and predict the infinite series of higher-order terms. For intermediate values of $\lambda n$ we find that $\Delta_n/n$ increases monotonically approaching a $(\lambda n)^{1/3}$ behavior in the $\lambda n \to \infty$ limit. We further generalize our results to the $\displaystyle{\left(\vec{\phi} \cdot \vec{\phi}\right)^{n/2}}$ operators in the $O(N)$ model., Comment: Added results for the O(N) model. 3 pages, two columns, one figure
- Published
- 2024