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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:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
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)

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