The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities
Abstract The contributions of the matter superfields and of the Faddeev-Popov ghosts to the β-function of N $$ \mathcal{N} $$ = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)192 |
| _version_ | 1818460860793749504 |
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| author | K. V. Stepanyantz |
| author_facet | K. V. Stepanyantz |
| author_sort | K. V. Stepanyantz |
| collection | DOAJ |
| description | Abstract The contributions of the matter superfields and of the Faddeev-Popov ghosts to the β-function of N $$ \mathcal{N} $$ = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the β-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the β-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev-Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices. |
| first_indexed | 2024-12-14T23:36:58Z |
| format | Article |
| id | doaj.art-744ad1259e9d423f83e1a2d723a5492f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T23:36:58Z |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-744ad1259e9d423f83e1a2d723a5492f2022-12-21T22:43:36ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114410.1007/JHEP01(2020)192The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularitiesK. V. Stepanyantz0Department of Theoretical Physics, Moscow State UniversityAbstract The contributions of the matter superfields and of the Faddeev-Popov ghosts to the β-function of N $$ \mathcal{N} $$ = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the β-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the β-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev-Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.https://doi.org/10.1007/JHEP01(2020)192Renormalization Regularization and RenormalonsSupersymmetric GaugeTheory |
| spellingShingle | K. V. Stepanyantz The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities Journal of High Energy Physics Renormalization Regularization and Renormalons Supersymmetric Gauge Theory |
| title | The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities |
| title_full | The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities |
| title_fullStr | The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities |
| title_full_unstemmed | The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities |
| title_short | The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities |
| title_sort | nsvz β function for theories regularized by higher covariant derivatives the all loop sum of matter and ghost singularities |
| topic | Renormalization Regularization and Renormalons Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP01(2020)192 |
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