Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality
Abstract Classically, the ground states of N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ℝ × S 3/Γ where Γ is a discrete ADE subgroup of SU(2) are represented by flat Wilson lines winding around the ADE singularity. By a duality relating such ground states to WZW conformal blocks, the...
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2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)037 |
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| author | Chao Ju |
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| author_sort | Chao Ju |
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| description | Abstract Classically, the ground states of N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ℝ × S 3/Γ where Γ is a discrete ADE subgroup of SU(2) are represented by flat Wilson lines winding around the ADE singularity. By a duality relating such ground states to WZW conformal blocks, the ground state degeneracy cannot be lifted by quantum corrections. Using the superconformal index, we compute the supersymmetric Casimir energy of each flat Wilson line for SU(2) SYM on different ADE singularities and find that the flat Wilson lines all have the same supersymmetric Casimir energy. We argue that this exact degeneracy is peculiar to N $$ \mathcal{N} $$ = 4 supersymmetry and show that the degeneracy is lifted when the number of supersymmetry is reduced. In particular, we uncover a surprising result for the ground state structure of the conformal N $$ \mathcal{N} $$ = 2 SU(2) four-flavor theory on S 3/Γ. For N $$ \mathcal{N} $$ = 4 SYM, S-duality maps the ground state Wilson lines to ground state t’ Hooft lines taking values in the Langlands dual group. We show that the supersymmetric Casimir energy of the t’ Hooft line ground states is the same as the Wilson line ground states. This can be viewed as a ground state test of S-duality. |
| format | Article |
| id | doaj-art-c8cd62455df14bc7b1c7dc739775c08d |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-c8cd62455df14bc7b1c7dc739775c08d2024-11-24T12:07:54ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024813810.1007/JHEP08(2024)037Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-dualityChao Ju0Berkeley Center for Theoretical Physics and Department of Physics, University of CaliforniaAbstract Classically, the ground states of N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ℝ × S 3/Γ where Γ is a discrete ADE subgroup of SU(2) are represented by flat Wilson lines winding around the ADE singularity. By a duality relating such ground states to WZW conformal blocks, the ground state degeneracy cannot be lifted by quantum corrections. Using the superconformal index, we compute the supersymmetric Casimir energy of each flat Wilson line for SU(2) SYM on different ADE singularities and find that the flat Wilson lines all have the same supersymmetric Casimir energy. We argue that this exact degeneracy is peculiar to N $$ \mathcal{N} $$ = 4 supersymmetry and show that the degeneracy is lifted when the number of supersymmetry is reduced. In particular, we uncover a surprising result for the ground state structure of the conformal N $$ \mathcal{N} $$ = 2 SU(2) four-flavor theory on S 3/Γ. For N $$ \mathcal{N} $$ = 4 SYM, S-duality maps the ground state Wilson lines to ground state t’ Hooft lines taking values in the Langlands dual group. We show that the supersymmetric Casimir energy of the t’ Hooft line ground states is the same as the Wilson line ground states. This can be viewed as a ground state test of S-duality.https://doi.org/10.1007/JHEP08(2024)037Duality in Gauge Field TheoriesSupersymmetric Gauge TheorySupersymmetry and DualityChern-Simons Theories |
| spellingShingle | Chao Ju Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality Journal of High Energy Physics Duality in Gauge Field Theories Supersymmetric Gauge Theory Supersymmetry and Duality Chern-Simons Theories |
| title | Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality |
| title_full | Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality |
| title_fullStr | Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality |
| title_full_unstemmed | Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality |
| title_short | Exact degeneracy of Casimir energy for N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ADE singularities and S-duality |
| title_sort | exact degeneracy of casimir energy for n mathcal n 4 supersymmetric yang mills theory on ade singularities and s duality |
| topic | Duality in Gauge Field Theories Supersymmetric Gauge Theory Supersymmetry and Duality Chern-Simons Theories |
| url | https://doi.org/10.1007/JHEP08(2024)037 |
| work_keys_str_mv | AT chaoju exactdegeneracyofcasimirenergyfornmathcaln4supersymmetricyangmillstheoryonadesingularitiesandsduality |