Constraints on beta functions in field theories

The \beta β -functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the \beta β -fun...

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Published inSciPost physics Vol. 12; no. 2; p. 046
Main Authors Ma, Han, Lee, Sung-Sik
Format Journal Article
LanguageEnglish
Published SciPost 01.02.2022
Online AccessGet full text
ISSN2542-4653
2542-4653
DOI10.21468/SciPostPhys.12.2.046

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Abstract The \beta β -functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the \beta β -functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the \beta β -functions defined in a measure zero subspace of couplings completely determine the \beta β -functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full \beta β -functions from the \beta β -functions defined in the subspace. As examples, we derive the full \beta β -functions for the O(N) O ( N ) vector model and the O_L(N) \times O_R(N) O L ( N ) × O R ( N ) matrix model entirely from the \beta β -functions defined in the subspace of single-trace couplings.
AbstractList The \beta β -functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the \beta β -functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the \beta β -functions defined in a measure zero subspace of couplings completely determine the \beta β -functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full \beta β -functions from the \beta β -functions defined in the subspace. As examples, we derive the full \beta β -functions for the O(N) O ( N ) vector model and the O_L(N) \times O_R(N) O L ( N ) × O R ( N ) matrix model entirely from the \beta β -functions defined in the subspace of single-trace couplings.
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the $\beta$-functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the $\beta$-functions defined in a measure zero subspace of couplings completely determine the $\beta$-functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full $\beta$-functions from the $\beta$-functions defined in the subspace. As examples, we derive the full $\beta$-functions for the $O(N)$ vector model and the $O_L(N) \times O_R(N)$ matrix model entirely from the $\beta$-functions defined in the subspace of single-trace couplings.
ArticleNumber 046
Author Ma, Han
Lee, Sung-Sik
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  organization: McMaster University, Perimeter Institute
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CitedBy_id crossref_primary_10_1103_PhysRevD_108_024054
crossref_primary_10_21468_SciPostPhys_15_3_111
crossref_primary_10_1103_PhysRevE_111_015304
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