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The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
by Cyril Closset, Elias Furrer, Adam Keyes, Osama Khlaif
Submission summary
| Authors (as registered SciPost users): | Cyril Closset · Elias Furrer · Osama Khlaif |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2501.11665v3 (pdf) |
| Date accepted: | Sept. 29, 2025 |
| Date submitted: | Sept. 9, 2025, 9:55 a.m. |
| Submitted by: | Cyril Closset |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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 $G=\widetilde G/\Gamma$, 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.
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Author comments upon resubmission
List of changes
-Added comments to paragraph after (2.37).
-Clarified the comment after (2.101) .
-Rewrote footnote 34 to correct a mistake.
-Clarified status of equation (3.91).
-Added SU(2) example in section 3.2.5.
-Added comment and reference to further work in progress at the end of section 1.
Published as SciPost Phys. 19, 106 (2025)