BPS states, conserved charges and centres of symmetric group algebras
Abstract In N $$ \mathcal{N} $$ = 4 SYM with U(N) gauge symmetry, the multiplicity of half-BPS states with fixed dimension can be labelled by Young diagrams and can be distinguished using conserved charges corresponding to Casimirs of U(N). The information theoretic study of LLM geometries and super...
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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)146 |
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| author | Garreth Kemp Sanjaye Ramgoolam |
| author_facet | Garreth Kemp Sanjaye Ramgoolam |
| author_sort | Garreth Kemp |
| collection | DOAJ |
| description | Abstract In N $$ \mathcal{N} $$ = 4 SYM with U(N) gauge symmetry, the multiplicity of half-BPS states with fixed dimension can be labelled by Young diagrams and can be distinguished using conserved charges corresponding to Casimirs of U(N). The information theoretic study of LLM geometries and superstars in the dual AdS5× S5 background has raised a number of questions about the distinguishability of Young diagrams when a finite set of Casimirs are known. Using Schur-Weyl duality relations between unitary groups and symmetric groups, these questions translate into structural questions about the centres of symmetric group algebras. We obtain algebraic and computational results about these structural properties and related Shannon entropies, and generate associated number sequences. A characterization of Young diagrams in terms of content distribution functions relates these number sequences to diophantine equations. These content distribution functions can be visualized as connected, segmented, open strings in content space. |
| format | Article |
| id | doaj-art-285f577e43de44dab808593cc51e9e88 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-285f577e43de44dab808593cc51e9e882025-01-26T12:11:14ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114310.1007/JHEP01(2020)146BPS states, conserved charges and centres of symmetric group algebrasGarreth Kemp0Sanjaye Ramgoolam1Department of Mathematics and Applied Mathematics, University of JohannesburgCentre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of LondonAbstract In N $$ \mathcal{N} $$ = 4 SYM with U(N) gauge symmetry, the multiplicity of half-BPS states with fixed dimension can be labelled by Young diagrams and can be distinguished using conserved charges corresponding to Casimirs of U(N). The information theoretic study of LLM geometries and superstars in the dual AdS5× S5 background has raised a number of questions about the distinguishability of Young diagrams when a finite set of Casimirs are known. Using Schur-Weyl duality relations between unitary groups and symmetric groups, these questions translate into structural questions about the centres of symmetric group algebras. We obtain algebraic and computational results about these structural properties and related Shannon entropies, and generate associated number sequences. A characterization of Young diagrams in terms of content distribution functions relates these number sequences to diophantine equations. These content distribution functions can be visualized as connected, segmented, open strings in content space.https://doi.org/10.1007/JHEP01(2020)146AdS-CFT CorrespondenceBlack Holes in String TheoryGauge-gravity correspondence |
| spellingShingle | Garreth Kemp Sanjaye Ramgoolam BPS states, conserved charges and centres of symmetric group algebras Journal of High Energy Physics AdS-CFT Correspondence Black Holes in String Theory Gauge-gravity correspondence |
| title | BPS states, conserved charges and centres of symmetric group algebras |
| title_full | BPS states, conserved charges and centres of symmetric group algebras |
| title_fullStr | BPS states, conserved charges and centres of symmetric group algebras |
| title_full_unstemmed | BPS states, conserved charges and centres of symmetric group algebras |
| title_short | BPS states, conserved charges and centres of symmetric group algebras |
| title_sort | bps states conserved charges and centres of symmetric group algebras |
| topic | AdS-CFT Correspondence Black Holes in String Theory Gauge-gravity correspondence |
| url | https://doi.org/10.1007/JHEP01(2020)146 |
| work_keys_str_mv | AT garrethkemp bpsstatesconservedchargesandcentresofsymmetricgroupalgebras AT sanjayeramgoolam bpsstatesconservedchargesandcentresofsymmetricgroupalgebras |