Convexity of charged operators in CFTs with multiple Abelian symmetries
Abstract Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the char...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2022)078 |
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| author | Eran Palti Adar Sharon |
| author_facet | Eran Palti Adar Sharon |
| author_sort | Eran Palti |
| collection | DOAJ |
| description | Abstract Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large. In this paper, we develop this constraint in the context of multiple Abelian global symmetries. We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large. In the special case of two-dimensional CFTs, the index can be made parametrically large, which we prove by an explicit example. However, we also prove that in two dimensions there always exist convex directions generating a sub-lattice with an index bounded by the current levels of the global symmetry. Therefore, in two dimensions, the conjecture should be slightly modified to account for the current levels, and then it can be proven. In more than two dimensions, we show that the index of the sub-lattice generated by marginally convex charge vectors associated to BPS operators only, can be made parametrically large. However, we do not find evidence for parametric delay in convexity once all operators are considered. |
| first_indexed | 2024-04-11T21:11:44Z |
| format | Article |
| id | doaj.art-2b9c3ba3bf5d4ea8bdd56a057d450888 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T21:11:44Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2b9c3ba3bf5d4ea8bdd56a057d4508882022-12-22T04:02:59ZengSpringerOpenJournal of High Energy Physics1029-84792022-09-012022912210.1007/JHEP09(2022)078Convexity of charged operators in CFTs with multiple Abelian symmetriesEran Palti0Adar Sharon1Department of Physics, Ben-Gurion University of the NegevDepartment of Particle Physics and Astrophysics, Weizmann Institute of ScienceAbstract Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large. In this paper, we develop this constraint in the context of multiple Abelian global symmetries. We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large. In the special case of two-dimensional CFTs, the index can be made parametrically large, which we prove by an explicit example. However, we also prove that in two dimensions there always exist convex directions generating a sub-lattice with an index bounded by the current levels of the global symmetry. Therefore, in two dimensions, the conjecture should be slightly modified to account for the current levels, and then it can be proven. In more than two dimensions, we show that the index of the sub-lattice generated by marginally convex charge vectors associated to BPS operators only, can be made parametrically large. However, we do not find evidence for parametric delay in convexity once all operators are considered.https://doi.org/10.1007/JHEP09(2022)078AdS-CFT CorrespondenceGlobal SymmetriesScale and Conformal Symmetries |
| spellingShingle | Eran Palti Adar Sharon Convexity of charged operators in CFTs with multiple Abelian symmetries Journal of High Energy Physics AdS-CFT Correspondence Global Symmetries Scale and Conformal Symmetries |
| title | Convexity of charged operators in CFTs with multiple Abelian symmetries |
| title_full | Convexity of charged operators in CFTs with multiple Abelian symmetries |
| title_fullStr | Convexity of charged operators in CFTs with multiple Abelian symmetries |
| title_full_unstemmed | Convexity of charged operators in CFTs with multiple Abelian symmetries |
| title_short | Convexity of charged operators in CFTs with multiple Abelian symmetries |
| title_sort | convexity of charged operators in cfts with multiple abelian symmetries |
| topic | AdS-CFT Correspondence Global Symmetries Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP09(2022)078 |
| work_keys_str_mv | AT eranpalti convexityofchargedoperatorsincftswithmultipleabeliansymmetries AT adarsharon convexityofchargedoperatorsincftswithmultipleabeliansymmetries |