Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory
Abstract In radial quantization, the ground states of a gauge theory on ADE singularities ℝ4 /Γ are characterized by flat connections that are maps from Γ to the gauge group. We study Class S $$ \mathcal{S} $$ theory of type a 1 $$ {\mathfrak{a}}_1 $$ = su 2 $$ \mathfrak{su}(2) $$ on a Riemann surfa...
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2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)219 |
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| author | Emil Albrychiewicz Andrés Franco Valiente Ori J. Ganor Chao Ju |
| author_facet | Emil Albrychiewicz Andrés Franco Valiente Ori J. Ganor Chao Ju |
| author_sort | Emil Albrychiewicz |
| collection | DOAJ |
| description | Abstract In radial quantization, the ground states of a gauge theory on ADE singularities ℝ4 /Γ are characterized by flat connections that are maps from Γ to the gauge group. We study Class S $$ \mathcal{S} $$ theory of type a 1 $$ {\mathfrak{a}}_1 $$ = su 2 $$ \mathfrak{su}(2) $$ on a Riemann surface of genus g > 1, without punctures. The fundamental building block of Class S $$ \mathcal{S} $$ theory is the trifundamental Trinion theory — a low energy limit of two M5 branes compactified on the three-punctured Riemann sphere. We show, through the superconformal index, that the supersymmetric Casimir energy of the trifundamental theory imposes a constraint on the set of allowed flat connections, which agrees with the prediction of a duality relating the ground state Hilbert space of Class S $$ \mathcal{S} $$ on ADE singularities to the Hilbert space of a certain dual Chern-Simons theory whose gauge group is given by the McKay correspondence. The conjecture is shown to hold for Γ = ℤ k , agreeing with the previous results of Benini et al. and Alday et al. A non-abelian generalization of this duality is analyzed by considering the example of the dicyclic group Γ = Dic2, corresponding to Chern-Simons gauge group SO(8). |
| format | Article |
| id | doaj-art-7dc47ec7eaf3433aac588aee0bd072c7 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-7dc47ec7eaf3433aac588aee0bd072c72024-12-08T12:13:14ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241014210.1007/JHEP10(2024)219Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theoryEmil Albrychiewicz0Andrés Franco Valiente1Ori J. Ganor2Chao Ju3Center for Theoretical Physics and Department of Physics, University of CaliforniaCenter for Theoretical Physics and Department of Physics, University of CaliforniaCenter for Theoretical Physics and Department of Physics, University of CaliforniaCenter for Theoretical Physics and Department of Physics, University of CaliforniaAbstract In radial quantization, the ground states of a gauge theory on ADE singularities ℝ4 /Γ are characterized by flat connections that are maps from Γ to the gauge group. We study Class S $$ \mathcal{S} $$ theory of type a 1 $$ {\mathfrak{a}}_1 $$ = su 2 $$ \mathfrak{su}(2) $$ on a Riemann surface of genus g > 1, without punctures. The fundamental building block of Class S $$ \mathcal{S} $$ theory is the trifundamental Trinion theory — a low energy limit of two M5 branes compactified on the three-punctured Riemann sphere. We show, through the superconformal index, that the supersymmetric Casimir energy of the trifundamental theory imposes a constraint on the set of allowed flat connections, which agrees with the prediction of a duality relating the ground state Hilbert space of Class S $$ \mathcal{S} $$ on ADE singularities to the Hilbert space of a certain dual Chern-Simons theory whose gauge group is given by the McKay correspondence. The conjecture is shown to hold for Γ = ℤ k , agreeing with the previous results of Benini et al. and Alday et al. A non-abelian generalization of this duality is analyzed by considering the example of the dicyclic group Γ = Dic2, corresponding to Chern-Simons gauge group SO(8).https://doi.org/10.1007/JHEP10(2024)219Chern-Simons TheoriesDuality in Gauge Field TheoriesSupersymmetric Gauge TheoryTopological Field Theories |
| spellingShingle | Emil Albrychiewicz Andrés Franco Valiente Ori J. Ganor Chao Ju Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory Journal of High Energy Physics Chern-Simons Theories Duality in Gauge Field Theories Supersymmetric Gauge Theory Topological Field Theories |
| title | Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory |
| title_full | Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory |
| title_fullStr | Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory |
| title_full_unstemmed | Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory |
| title_short | Ground states of Class S $$ \mathcal{S} $$ theory on ADE singularities and dual Chern-Simons theory |
| title_sort | ground states of class s mathcal s theory on ade singularities and dual chern simons theory |
| topic | Chern-Simons Theories Duality in Gauge Field Theories Supersymmetric Gauge Theory Topological Field Theories |
| url | https://doi.org/10.1007/JHEP10(2024)219 |
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