Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation

Mandric, Vlad-Mihai, Morris, Tim R. and Stulga, Dalius (2023) Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation 19pp. (doi:10.48550/arXiv.2306.14643).

Record type: Monograph (Working Paper)

Abstract

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 dn of high dimension potential-type operators On(φ) around a non-trivial fixed point. We find that dn=n(d−dφ) to leading order in n as n→∞, where dφ=12(d−2+η) is the scaling dimension of the field, φ, 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≥0 and additionally for N=−2,−4,…. These results are universal, independent of the choice of cutoff function which we keep general throughout, subject only to some weak constraints.

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2306.14643v1 - Author's Original

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