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Constraints on beta functions in field theories
by Han Ma, Sung-Sik Lee
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Submission summary
| Authors (as registered SciPost users): | Sung-Sik Lee · Han Ma |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2009.11880v5 (pdf) |
| Date accepted: | 2021-11-02 |
| Date submitted: | 2021-10-11 21:57 |
| Submitted by: | Ma, Han |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
List of changes
We have added a paragraph that lists open questions and future directions in the conclusion of the revised manuscript.
Published as SciPost Phys. 12, 046 (2022)