Scaling dimensions in QED3 from the ϵ-expansion
Abstract We study the fixed point that controls the IR dynamics of QED in d = 4 − 2ϵ dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the ϵ-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that wa...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP12(2017)054 |
| _version_ | 1818060282875871232 |
|---|---|
| author | Lorenzo Di Pietro Emmanuel Stamou |
| author_facet | Lorenzo Di Pietro Emmanuel Stamou |
| author_sort | Lorenzo Di Pietro |
| collection | DOAJ |
| description | Abstract We study the fixed point that controls the IR dynamics of QED in d = 4 − 2ϵ dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the ϵ-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to d = 3 to estimate their value at the IR fixed point of QED3 as function of the number of fermions N f . The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of N f , which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, the ϵ-expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of N f . |
| first_indexed | 2024-12-10T13:29:57Z |
| format | Article |
| id | doaj.art-11afa68471994308bfe644dd47beaace |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T13:29:57Z |
| publishDate | 2017-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-11afa68471994308bfe644dd47beaace2022-12-22T01:46:59ZengSpringerOpenJournal of High Energy Physics1029-84792017-12-0120171213610.1007/JHEP12(2017)054Scaling dimensions in QED3 from the ϵ-expansionLorenzo Di Pietro0Emmanuel Stamou1Perimeter Institute for Theoretical PhysicsEnrico Fermi Institute, University of ChicagoAbstract We study the fixed point that controls the IR dynamics of QED in d = 4 − 2ϵ dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the ϵ-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to d = 3 to estimate their value at the IR fixed point of QED3 as function of the number of fermions N f . The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of N f , which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, the ϵ-expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of N f .http://link.springer.com/article/10.1007/JHEP12(2017)054Conformal Field TheoryField Theories in Lower DimensionsRenormalization Group |
| spellingShingle | Lorenzo Di Pietro Emmanuel Stamou Scaling dimensions in QED3 from the ϵ-expansion Journal of High Energy Physics Conformal Field Theory Field Theories in Lower Dimensions Renormalization Group |
| title | Scaling dimensions in QED3 from the ϵ-expansion |
| title_full | Scaling dimensions in QED3 from the ϵ-expansion |
| title_fullStr | Scaling dimensions in QED3 from the ϵ-expansion |
| title_full_unstemmed | Scaling dimensions in QED3 from the ϵ-expansion |
| title_short | Scaling dimensions in QED3 from the ϵ-expansion |
| title_sort | scaling dimensions in qed3 from the ϵ expansion |
| topic | Conformal Field Theory Field Theories in Lower Dimensions Renormalization Group |
| url | http://link.springer.com/article/10.1007/JHEP12(2017)054 |
| work_keys_str_mv | AT lorenzodipietro scalingdimensionsinqed3fromtheeexpansion AT emmanuelstamou scalingdimensionsinqed3fromtheeexpansion |