Ground States of Class S Theory on ADE Singularities and dual Chern-Simons theory
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
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2024
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| _version_ | 1866913493492432896 |
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| author | Albrychiewicz, Emil Valiente, Andrés Franco Ganor, Ori J. Ju, Chao |
| author_facet | Albrychiewicz, Emil Valiente, Andrés Franco Ganor, Ori J. Ju, Chao |
| contents | In radial quantization, the ground states of a gauge theory on ADE singularities $\mathbb{R}^4/Γ$ are characterized by flat connections that are maps from $Γ$ to the gauge group. We study Class $\mathcal{S}$ theory of type $\mathfrak{a}_1=\mathfrak{su}(2)$ on a Riemann surface of genus $g>1$, without punctures. The fundamental building block of Class $\mathcal{S}$ 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 $\mathcal{S}$ 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 $Γ=\mathbb{Z}_k$, 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 $Γ=\text{Dic}_2$, corresponding to Chern-Simons gauge group SO$(8)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ground States of Class S Theory on ADE Singularities and dual Chern-Simons theory Albrychiewicz, Emil Valiente, Andrés Franco Ganor, Ori J. Ju, Chao High Energy Physics - Theory In radial quantization, the ground states of a gauge theory on ADE singularities $\mathbb{R}^4/Γ$ are characterized by flat connections that are maps from $Γ$ to the gauge group. We study Class $\mathcal{S}$ theory of type $\mathfrak{a}_1=\mathfrak{su}(2)$ on a Riemann surface of genus $g>1$, without punctures. The fundamental building block of Class $\mathcal{S}$ 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 $\mathcal{S}$ 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 $Γ=\mathbb{Z}_k$, 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 $Γ=\text{Dic}_2$, corresponding to Chern-Simons gauge group SO$(8)$. |
| title | Ground States of Class S Theory on ADE Singularities and dual Chern-Simons theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.12446 |