Modular constraints on superconformal field theories
We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γθ congruence subgroup of the full modular group SL(2, ℤ). We employ semi-definite programming to find constraints on the...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2019
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| _version_ | 1797094258535038976 |
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| author | Bae, J-B Lee, S Song, J |
| author_facet | Bae, J-B Lee, S Song, J |
| author_sort | Bae, J-B |
| collection | OXFORD |
| description | We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γθ congruence subgroup of the full modular group SL(2, ℤ). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U(1) charges. Especially, the upper bounds on the twist gap for the noncurrent primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γθ. Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS3.
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| first_indexed | 2024-03-07T04:11:34Z |
| format | Journal article |
| id | oxford-uuid:c7ff8300-c84d-4a32-8471-eed71b3c75c2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:11:34Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:c7ff8300-c84d-4a32-8471-eed71b3c75c22022-03-27T06:49:13ZModular constraints on superconformal field theoriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c7ff8300-c84d-4a32-8471-eed71b3c75c2EnglishSymplectic ElementsSpringer2019Bae, J-BLee, SSong, JWe constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γθ congruence subgroup of the full modular group SL(2, ℤ). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U(1) charges. Especially, the upper bounds on the twist gap for the noncurrent primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γθ. Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS3. |
| spellingShingle | Bae, J-B Lee, S Song, J Modular constraints on superconformal field theories |
| title | Modular constraints on superconformal field theories |
| title_full | Modular constraints on superconformal field theories |
| title_fullStr | Modular constraints on superconformal field theories |
| title_full_unstemmed | Modular constraints on superconformal field theories |
| title_short | Modular constraints on superconformal field theories |
| title_sort | modular constraints on superconformal field theories |
| work_keys_str_mv | AT baejb modularconstraintsonsuperconformalfieldtheories AT lees modularconstraintsonsuperconformalfieldtheories AT songj modularconstraintsonsuperconformalfieldtheories |