Combinatoric topological string theories and group theory algorithms
Abstract A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on Dijkgraaf-Witten theory of flat G-bundles on surfaces. We e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2022)147 |
| _version_ | 1798030866524405760 |
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| author | Sanjaye Ramgoolam Eric Sharpe |
| author_facet | Sanjaye Ramgoolam Eric Sharpe |
| author_sort | Sanjaye Ramgoolam |
| collection | DOAJ |
| description | Abstract A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on Dijkgraaf-Witten theory of flat G-bundles on surfaces. We extend this result to projective representations of G using twisted Dijkgraaf-Witten theory. New algorithms for characters are described, based on handle creation operators and minimal multiplicative generating subspaces for the centers of group algebras and twisted group algebras. Such minimal generating subspaces are of interest in connection with information theoretic aspects of the AdS/CFT correspondence. For the untwisted case, we describe the integrality properties of certain character sums and character power sums which follow from these constructive G-CTST algorithms. These integer sums appear as residues of singularities in G-CTST generating functions. S-duality of the combinatoric topological strings motivates the definition of an inverse handle creation operator in the centers of group algebras and twisted group algebras. |
| first_indexed | 2024-04-11T19:48:11Z |
| format | Article |
| id | doaj.art-835cb0249a2f4182aa40786026b3cf40 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T19:48:11Z |
| publishDate | 2022-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-835cb0249a2f4182aa40786026b3cf402022-12-22T04:06:23ZengSpringerOpenJournal of High Energy Physics1029-84792022-10-0120221015810.1007/JHEP10(2022)147Combinatoric topological string theories and group theory algorithmsSanjaye Ramgoolam0Eric Sharpe1Centre for Theoretical Physics, Department of Physics, Queen Mary University of LondonDepartment of Physics MC 0435, 850 West Campus Drive Virginia TechAbstract A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on Dijkgraaf-Witten theory of flat G-bundles on surfaces. We extend this result to projective representations of G using twisted Dijkgraaf-Witten theory. New algorithms for characters are described, based on handle creation operators and minimal multiplicative generating subspaces for the centers of group algebras and twisted group algebras. Such minimal generating subspaces are of interest in connection with information theoretic aspects of the AdS/CFT correspondence. For the untwisted case, we describe the integrality properties of certain character sums and character power sums which follow from these constructive G-CTST algorithms. These integer sums appear as residues of singularities in G-CTST generating functions. S-duality of the combinatoric topological strings motivates the definition of an inverse handle creation operator in the centers of group algebras and twisted group algebras.https://doi.org/10.1007/JHEP10(2022)147Discrete SymmetriesTopological Field TheoriesAdS-CFT CorrespondenceTopological Strings |
| spellingShingle | Sanjaye Ramgoolam Eric Sharpe Combinatoric topological string theories and group theory algorithms Journal of High Energy Physics Discrete Symmetries Topological Field Theories AdS-CFT Correspondence Topological Strings |
| title | Combinatoric topological string theories and group theory algorithms |
| title_full | Combinatoric topological string theories and group theory algorithms |
| title_fullStr | Combinatoric topological string theories and group theory algorithms |
| title_full_unstemmed | Combinatoric topological string theories and group theory algorithms |
| title_short | Combinatoric topological string theories and group theory algorithms |
| title_sort | combinatoric topological string theories and group theory algorithms |
| topic | Discrete Symmetries Topological Field Theories AdS-CFT Correspondence Topological Strings |
| url | https://doi.org/10.1007/JHEP10(2022)147 |
| work_keys_str_mv | AT sanjayeramgoolam combinatorictopologicalstringtheoriesandgrouptheoryalgorithms AT ericsharpe combinatorictopologicalstringtheoriesandgrouptheoryalgorithms |