Refined half-integer condition on RG flows
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910026504863744 |
|---|---|
| author | Kikuchi, Ken |
| author_facet | Kikuchi, Ken |
| contents | Renormalization group flows are constrained by symmetries. Traditionally, we have made the most of 't Hooft anomalies associated to the symmetries. The anomaly is mathematically part of the data for the monoidal structure on symmetry categories. The symmetry categories sometimes admit additional structures such as braiding. It was found that the additional structures give further constraints on renormalization group flows. One of these constraints is the half-integer condition. The condition claims the following. Braidings are characterized by conformal dimensions. A symmetry object $c$ in a braided symmetry category surviving all along the flow thus has two conformal dimensions, one in ultraviolet $h_c^\text{UV}$ and the other in infrared $h_c^\text{IR}$. In a renormalization group flow with a renormalization group defect, they add up to a half-integer $h_c^\text{UV}+h_c^\text{IR}\in\frac12\mathbb Z$. We find a necessary condition for the sum to be half-integer. We solve some flows with the refined half-integer condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12085 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined half-integer condition on RG flows Kikuchi, Ken High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra Renormalization group flows are constrained by symmetries. Traditionally, we have made the most of 't Hooft anomalies associated to the symmetries. The anomaly is mathematically part of the data for the monoidal structure on symmetry categories. The symmetry categories sometimes admit additional structures such as braiding. It was found that the additional structures give further constraints on renormalization group flows. One of these constraints is the half-integer condition. The condition claims the following. Braidings are characterized by conformal dimensions. A symmetry object $c$ in a braided symmetry category surviving all along the flow thus has two conformal dimensions, one in ultraviolet $h_c^\text{UV}$ and the other in infrared $h_c^\text{IR}$. In a renormalization group flow with a renormalization group defect, they add up to a half-integer $h_c^\text{UV}+h_c^\text{IR}\in\frac12\mathbb Z$. We find a necessary condition for the sum to be half-integer. We solve some flows with the refined half-integer condition. |
| title | Refined half-integer condition on RG flows |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2602.12085 |