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 in | SciPost physics Vol. 12; no. 2; p. 046 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
SciPost
01.02.2022
|
| Online Access | Get full text |
| ISSN | 2542-4653 2542-4653 |
| DOI | 10.21468/SciPostPhys.12.2.046 |
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| Summary: | 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. |
|---|---|
| ISSN: | 2542-4653 2542-4653 |
| DOI: | 10.21468/SciPostPhys.12.2.046 |