TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.2.046
TI  - Constraints on beta functions in field theories
PY  - 2022/02/01
UR  - https://www.scipost.org/SciPostPhys.12.2.046
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 2
SP  - 046
A1  - Ma, Han
AU  - Lee, Sung-Sik
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.12.2.046,
	title={{Constraints on beta functions in field theories}},
	author={Han Ma and Sung-Sik Lee},
	journal={SciPost Phys.},
	volume={12},
	pages={046},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.2.046},
	url={https://scipost.org/10.21468/SciPostPhys.12.2.046},
}