Chern-Simons theory, Ehrhart polynomials, and representation theory
Abstract The Hilbert space of level q Chern-Simons theory of gauge group G of the ADE type quantized on T 2 can be represented by points that lie on the weight lattice of the Lie algebra g up to some discrete identifications. Of special significance are the points that also lie on the root lattice....
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2024)052 |
| _version_ | 1827265074490769408 |
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| author | Chao Ju |
| author_facet | Chao Ju |
| author_sort | Chao Ju |
| collection | DOAJ |
| description | Abstract The Hilbert space of level q Chern-Simons theory of gauge group G of the ADE type quantized on T 2 can be represented by points that lie on the weight lattice of the Lie algebra g up to some discrete identifications. Of special significance are the points that also lie on the root lattice. The generating functions that count the number of such points are quasi-periodic Ehrhart polynomials which coincide with the generating functions of SU(q) representation of the ADE subgroups of SU(2) given by the McKay correspondence. This coincidence has roots in a string/M theory construction where D3(M5)-branes are put along an ADE singularity. Finally, a new perspective on the McKay correspondence that involves the inverse of the Cartan matrices is proposed. |
| first_indexed | 2024-03-08T14:20:41Z |
| format | Article |
| id | doaj.art-f5a35d69faac4fcf93181247f7f53478 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-22T03:56:10Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f5a35d69faac4fcf93181247f7f534782024-04-28T11:06:49ZengSpringerOpenJournal of High Energy Physics1029-84792024-01-012024112810.1007/JHEP01(2024)052Chern-Simons theory, Ehrhart polynomials, and representation theoryChao Ju0Berkeley Center for Theoretical Physics and Department of Physics, University of CaliforniaAbstract The Hilbert space of level q Chern-Simons theory of gauge group G of the ADE type quantized on T 2 can be represented by points that lie on the weight lattice of the Lie algebra g up to some discrete identifications. Of special significance are the points that also lie on the root lattice. The generating functions that count the number of such points are quasi-periodic Ehrhart polynomials which coincide with the generating functions of SU(q) representation of the ADE subgroups of SU(2) given by the McKay correspondence. This coincidence has roots in a string/M theory construction where D3(M5)-branes are put along an ADE singularity. Finally, a new perspective on the McKay correspondence that involves the inverse of the Cartan matrices is proposed.https://doi.org/10.1007/JHEP01(2024)052Chern-Simons TheoriesDuality in Gauge Field TheoriesAdS-CFT CorrespondenceM-Theory |
| spellingShingle | Chao Ju Chern-Simons theory, Ehrhart polynomials, and representation theory Journal of High Energy Physics Chern-Simons Theories Duality in Gauge Field Theories AdS-CFT Correspondence M-Theory |
| title | Chern-Simons theory, Ehrhart polynomials, and representation theory |
| title_full | Chern-Simons theory, Ehrhart polynomials, and representation theory |
| title_fullStr | Chern-Simons theory, Ehrhart polynomials, and representation theory |
| title_full_unstemmed | Chern-Simons theory, Ehrhart polynomials, and representation theory |
| title_short | Chern-Simons theory, Ehrhart polynomials, and representation theory |
| title_sort | chern simons theory ehrhart polynomials and representation theory |
| topic | Chern-Simons Theories Duality in Gauge Field Theories AdS-CFT Correspondence M-Theory |
| url | https://doi.org/10.1007/JHEP01(2024)052 |
| work_keys_str_mv | AT chaoju chernsimonstheoryehrhartpolynomialsandrepresentationtheory |