Implications of ANEC for SCFTs in four dimensions
Abstract We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions ∆ of operators in four-dimensional N $$ \mathcal{N} $$ = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on ∆. We anal...
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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)093 |
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| author | Andrea Manenti Andreas Stergiou Alessandro Vichi |
| author_facet | Andrea Manenti Andreas Stergiou Alessandro Vichi |
| author_sort | Andrea Manenti |
| collection | DOAJ |
| description | Abstract We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions ∆ of operators in four-dimensional N $$ \mathcal{N} $$ = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on ∆. We analyze in detail chiral operators in the 1 2 j 0 $$ \left(\frac{1}{2}j,0\right) $$ Lorentz representation and prove that the ANEC implies the lower bound Δ ≥ 3 2 j $$ \Delta \ge \frac{3}{2}j $$ , which is stronger than the corresponding unitarity bound for j > 1. We also derive ANEC bounds on 1 2 j 0 $$ \left(\frac{1}{2}j,0\right) $$ operators obeying other possible shortening conditions, as well as general 1 2 j 0 $$ \left(\frac{1}{2}j,0\right) $$ operators not obeying any shortening condition. In both cases we find that they are typically stronger than the corresponding unitarity bounds. Finally, we elucidate operator-dimension constraints that follow from our N $$ \mathcal{N} $$ = 1 results for multiplets of N $$ \mathcal{N} $$ = 2, 4 superconformal theories in four dimensions. By recasting the ANEC as a convex optimization problem and using standard semidefinite programming methods we are able to improve on previous analyses in the literature pertaining to the nonsupersymmetric case. |
| format | Article |
| id | doaj-art-dca91d61210f4301ac344203cefac2d8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-dca91d61210f4301ac344203cefac2d82025-01-26T12:11:18ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114110.1007/JHEP01(2020)093Implications of ANEC for SCFTs in four dimensionsAndrea Manenti0Andreas Stergiou1Alessandro Vichi2Institute of Physics, École Polytechnique Fédérale de LausanneTheoretical Division, MS B285, Los Alamos National LaboratoryInstitute of Physics, École Polytechnique Fédérale de LausanneAbstract We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions ∆ of operators in four-dimensional N $$ \mathcal{N} $$ = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on ∆. We analyze in detail chiral operators in the 1 2 j 0 $$ \left(\frac{1}{2}j,0\right) $$ Lorentz representation and prove that the ANEC implies the lower bound Δ ≥ 3 2 j $$ \Delta \ge \frac{3}{2}j $$ , which is stronger than the corresponding unitarity bound for j > 1. We also derive ANEC bounds on 1 2 j 0 $$ \left(\frac{1}{2}j,0\right) $$ operators obeying other possible shortening conditions, as well as general 1 2 j 0 $$ \left(\frac{1}{2}j,0\right) $$ operators not obeying any shortening condition. In both cases we find that they are typically stronger than the corresponding unitarity bounds. Finally, we elucidate operator-dimension constraints that follow from our N $$ \mathcal{N} $$ = 1 results for multiplets of N $$ \mathcal{N} $$ = 2, 4 superconformal theories in four dimensions. By recasting the ANEC as a convex optimization problem and using standard semidefinite programming methods we are able to improve on previous analyses in the literature pertaining to the nonsupersymmetric case.https://doi.org/10.1007/JHEP01(2020)093Conformal Field TheorySuperspaces |
| spellingShingle | Andrea Manenti Andreas Stergiou Alessandro Vichi Implications of ANEC for SCFTs in four dimensions Journal of High Energy Physics Conformal Field Theory Superspaces |
| title | Implications of ANEC for SCFTs in four dimensions |
| title_full | Implications of ANEC for SCFTs in four dimensions |
| title_fullStr | Implications of ANEC for SCFTs in four dimensions |
| title_full_unstemmed | Implications of ANEC for SCFTs in four dimensions |
| title_short | Implications of ANEC for SCFTs in four dimensions |
| title_sort | implications of anec for scfts in four dimensions |
| topic | Conformal Field Theory Superspaces |
| url | https://doi.org/10.1007/JHEP01(2020)093 |
| work_keys_str_mv | AT andreamanenti implicationsofanecforscftsinfourdimensions AT andreasstergiou implicationsofanecforscftsinfourdimensions AT alessandrovichi implicationsofanecforscftsinfourdimensions |