The 3d $A$-model and generalised symmetries, part I: Bosonic Chern-Simons theories

Journal article

The 3d AA-model is a two-dimensional approach to the computation of supersymmetric observables of three-dimensional \mathcal{N}=2𝒩=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 GG̃ 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/\GammaG=G̃/Γ, which is obtained from the \widetilde GG̃ theory by gauging a discrete one-form symmetry. In this paper, we discuss in detail the case of pure \mathcal{N}=2𝒩=2 Chern-Simons theories (without matter) for simple groups GG. When G=\widetilde GG=G̃ 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_kG̃k, 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_kGk can be obtained from \widetilde G_kG̃k by the condensation of abelian anyons which are bosonic. Along the way, we revisit the 3d AA-model formalism by emphasising its 2d TQFT underpinning.

Authors: Closset, C; Furrer, E; Keyes, A; Khlaif, O

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: SciPost
• Journal: SciPost Physics
• Volume: 19
• Issue: 4
• Article number: 106
• Publication date: 2025-10-21
• Acceptance date: 2025-09-29
• DOI: 10.21468/scipostphys.19.4.106
• EISSN: 2542-4653
• ISSN: 2542-4653
• Language: English