Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops
Abstract We consider a one-loop finite $$\mathcal{N}=1$$ N = 1 supersymmetric theory in such a renormalization scheme that the first L contributions to the gauge $$\beta $$ β -function and the first $$(L-1)$$ ( L - 1 ) contributions to the anomalous dimension of the matter superfields and to the Yuk...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-07-01
|
| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-021-09363-7 |
| _version_ | 1819145711883649024 |
|---|---|
| author | K. V. Stepanyantz |
| author_facet | K. V. Stepanyantz |
| author_sort | K. V. Stepanyantz |
| collection | DOAJ |
| description | Abstract We consider a one-loop finite $$\mathcal{N}=1$$ N = 1 supersymmetric theory in such a renormalization scheme that the first L contributions to the gauge $$\beta $$ β -function and the first $$(L-1)$$ ( L - 1 ) contributions to the anomalous dimension of the matter superfields and to the Yukawa $$\beta $$ β -function vanish. It is demonstrated that in this case the NSVZ equation and the exact equation for the Yukawa $$\beta $$ β -function in the first nontrivial order are valid for an arbitrary renormalization prescription respecting the above assumption. This implies that under this assumption the $$(L+1)$$ ( L + 1 ) -loop contribution to the gauge $$\beta $$ β -function and the L-loop contribution to the Yukawa $$\beta $$ β -function are always expressed in terms of the L-loop contribution to the anomalous dimension of the matter superfields. This statement generalizes the result of Grisaru, Milewski, and Zanon that for a theory finite in L loops the $$(L+1)$$ ( L + 1 ) -loop contribution to the $$\beta $$ β -function also vanishes. In particular, it gives a simple explanation why their result is valid although the NSVZ equation does not hold in an arbitrary subtraction scheme. |
| first_indexed | 2024-12-22T13:02:23Z |
| format | Article |
| id | doaj.art-8255070f37b94138891de43a430ef6ab |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-22T13:02:23Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-8255070f37b94138891de43a430ef6ab2022-12-21T18:24:57ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-07-0181711110.1140/epjc/s10052-021-09363-7Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loopsK. V. Stepanyantz0Faculty of Physics, Department of Theoretical Physics, Moscow State UniversityAbstract We consider a one-loop finite $$\mathcal{N}=1$$ N = 1 supersymmetric theory in such a renormalization scheme that the first L contributions to the gauge $$\beta $$ β -function and the first $$(L-1)$$ ( L - 1 ) contributions to the anomalous dimension of the matter superfields and to the Yukawa $$\beta $$ β -function vanish. It is demonstrated that in this case the NSVZ equation and the exact equation for the Yukawa $$\beta $$ β -function in the first nontrivial order are valid for an arbitrary renormalization prescription respecting the above assumption. This implies that under this assumption the $$(L+1)$$ ( L + 1 ) -loop contribution to the gauge $$\beta $$ β -function and the L-loop contribution to the Yukawa $$\beta $$ β -function are always expressed in terms of the L-loop contribution to the anomalous dimension of the matter superfields. This statement generalizes the result of Grisaru, Milewski, and Zanon that for a theory finite in L loops the $$(L+1)$$ ( L + 1 ) -loop contribution to the $$\beta $$ β -function also vanishes. In particular, it gives a simple explanation why their result is valid although the NSVZ equation does not hold in an arbitrary subtraction scheme.https://doi.org/10.1140/epjc/s10052-021-09363-7 |
| spellingShingle | K. V. Stepanyantz Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops European Physical Journal C: Particles and Fields |
| title | Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops |
| title_full | Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops |
| title_fullStr | Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops |
| title_full_unstemmed | Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops |
| title_short | Exact $$\beta $$ β -functions for $$\mathcal{N}=1$$ N = 1 supersymmetric theories finite in the lowest loops |
| title_sort | exact beta β functions for mathcal n 1 n 1 supersymmetric theories finite in the lowest loops |
| url | https://doi.org/10.1140/epjc/s10052-021-09363-7 |
| work_keys_str_mv | AT kvstepanyantz exactbetabfunctionsformathcaln1n1supersymmetrictheoriesfiniteinthelowestloops |