Revisiting the dilatation operator of the Wilson–Fisher fixed point
We revisit the order-ε dilatation operator of the Wilson–Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction t...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2017-07-01
|
| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321317301505 |
| _version_ | 1811261054408196096 |
|---|---|
| author | Pedro Liendo |
| author_facet | Pedro Liendo |
| author_sort | Pedro Liendo |
| collection | DOAJ |
| description | We revisit the order-ε dilatation operator of the Wilson–Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-ε scaling dimensions of the Wilson–Fisher fixed point can be fixed by symmetry. |
| first_indexed | 2024-04-12T18:56:45Z |
| format | Article |
| id | doaj.art-87182f57b40c499c96f0a1dda973d8eb |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-04-12T18:56:45Z |
| publishDate | 2017-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-87182f57b40c499c96f0a1dda973d8eb2022-12-22T03:20:17ZengElsevierNuclear Physics B0550-32131873-15622017-07-01920C36838410.1016/j.nuclphysb.2017.04.020Revisiting the dilatation operator of the Wilson–Fisher fixed pointPedro LiendoWe revisit the order-ε dilatation operator of the Wilson–Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-ε scaling dimensions of the Wilson–Fisher fixed point can be fixed by symmetry.http://www.sciencedirect.com/science/article/pii/S0550321317301505 |
| spellingShingle | Pedro Liendo Revisiting the dilatation operator of the Wilson–Fisher fixed point Nuclear Physics B |
| title | Revisiting the dilatation operator of the Wilson–Fisher fixed point |
| title_full | Revisiting the dilatation operator of the Wilson–Fisher fixed point |
| title_fullStr | Revisiting the dilatation operator of the Wilson–Fisher fixed point |
| title_full_unstemmed | Revisiting the dilatation operator of the Wilson–Fisher fixed point |
| title_short | Revisiting the dilatation operator of the Wilson–Fisher fixed point |
| title_sort | revisiting the dilatation operator of the wilson fisher fixed point |
| url | http://www.sciencedirect.com/science/article/pii/S0550321317301505 |
| work_keys_str_mv | AT pedroliendo revisitingthedilatationoperatorofthewilsonfisherfixedpoint |