Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
| Autor: | Mandric, Vlad-Mihai, Morris, Tim R., Stulga, Dalius |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.108.105003 |
| Popis: | We study $d$-dimensional scalar field theory in the Local Potential Approximation of the functional renormalization group. Sturm-Liouville methods allow the eigenoperator equation to be cast as a Schrodinger-type equation. Combining solutions in the large field limit with the Wentzel-Kramers-Brillouin approximation, we solve analytically for the scaling dimension $d_n$ of high dimension potential-type operators $\mathcal{O}_n(\varphi)$ around a non-trivial fixed point. We find that $d_n = n(d-d_\varphi)$ to leading order in $n$ as $n \to \infty$, where $d_\varphi=\frac{1}{2}(d-2+\eta)$ is the scaling dimension of the field, $\varphi$, and determine the power-law growth of the subleading correction. For $O(N)$ invariant scalar field theory, the scaling dimension is just double this, for all fixed $N\geq0$ and additionally for $N=-2,-4,\ldots \,.$ These results are universal, independent of the choice of cutoff function which we keep general throughout, subject only to some weak constraints. Comment: 23 pages, no figures. Clarifications added. Version published in PRD |
| Databáze: | arXiv |
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