The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914105501155328 |
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| author | Closset, Cyril Furrer, Elias Keyes, Adam Khlaif, Osama |
| author_facet | Closset, Cyril Furrer, Elias Keyes, Adam Khlaif, Osama |
| contents | The 3d $A$-model is a two-dimensional approach to the computation of supersymmetric observables of three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. In principle, it allows us to compute half-BPS partition functions on any compact Seifert three-manifold (as well as of expectation values of half-BPS lines thereon), but previous results focussed on the case where the gauge group $\widetilde G$ is a product of simply-connected and/or unitary gauge groups. We are interested in the more general case of a compact gauge group $G=\widetilde G/Γ$, which is obtained from the $\widetilde G$ theory by gauging a discrete one-form symmetry. In this paper, we discuss in detail the case of pure $\mathcal{N}=2$ Chern-Simons theories (without matter) for simple groups $G$. When $G=\widetilde G$ is simply-connected, we demonstrate the exact matching between the supersymmetric approach in terms of Seifert fibering operators and the 3d TQFT approach based on topological surgery in the infrared Chern-Simons theory $\widetilde G_k$, including through the identification of subtle counterterms that relate the two approaches. We then extend this discussion to the case where the Chern-Simons theory $G_k$ can be obtained from $\widetilde G_k$ by the condensation of abelian anyons which are bosonic. Along the way, we revisit the 3d $A$-model formalism by emphasising its 2d TQFT underpinning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories Closset, Cyril Furrer, Elias Keyes, Adam Khlaif, Osama High Energy Physics - Theory The 3d $A$-model is a two-dimensional approach to the computation of supersymmetric observables of three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. In principle, it allows us to compute half-BPS partition functions on any compact Seifert three-manifold (as well as of expectation values of half-BPS lines thereon), but previous results focussed on the case where the gauge group $\widetilde G$ is a product of simply-connected and/or unitary gauge groups. We are interested in the more general case of a compact gauge group $G=\widetilde G/Γ$, which is obtained from the $\widetilde G$ theory by gauging a discrete one-form symmetry. In this paper, we discuss in detail the case of pure $\mathcal{N}=2$ Chern-Simons theories (without matter) for simple groups $G$. When $G=\widetilde G$ is simply-connected, we demonstrate the exact matching between the supersymmetric approach in terms of Seifert fibering operators and the 3d TQFT approach based on topological surgery in the infrared Chern-Simons theory $\widetilde G_k$, including through the identification of subtle counterterms that relate the two approaches. We then extend this discussion to the case where the Chern-Simons theory $G_k$ can be obtained from $\widetilde G_k$ by the condensation of abelian anyons which are bosonic. Along the way, we revisit the 3d $A$-model formalism by emphasising its 2d TQFT underpinning. |
| title | The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.11665 |