3d-3d correspondence for mapping tori

Abstract

One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d $N=2$ SCFT $T[M_3]$ --- or, rather, a "collection of SCFTs" as we refer to it in the paper --- for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on $M_3$ and, secondly, is not limited to a particular supersymmetric partition function of $T[M_3]$. In particular, we propose to describe such "collection of SCFTs" in terms of 3d $N=2$ gauge theories with "non-linear matter'' fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of $T[M_3]$, and propose new tools to compute more recent $q$-series invariants $\hat{Z}(M_3)$ in the case of manifolds with $b_1>0$. Although we use genus-1 mapping tori as our "case study," many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.

arXiv comment53 pages, 8 figures

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Cited by in corpus (17)

• Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
• A slow review of the AGT correspondence
• $\hat{Z}$ at large $N$: from curve counts to quantum modularity
• Large color $R$-matrix for knot complements and strange identities
• Quivers for 3-manifolds: the correspondence, BPS states, and 3d $\mathcal{N}$=2 theories
• Higher rank $\hat{Z}$ and $F_K$
• Branches, quivers, and ideals for knot complements
• Cobordism invariants from BPS q-series
• Seiberg-like dualities for orthogonal and symplectic 3d $\mathcal{N}=2$ gauge theories with boundaries
• Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $\Sigma (2,3,6n+5)$
• Decomposition squared
• 3D-3D Correspondence from Seifert Fibering Operators
• Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums
• $c_{\mathrm{eff}}$ from Resurgence at the Stokes Line
• Non-Semisimple TQFT's and BPS $q$-Series
• Aspects of 4d supersymmetric dynamics and geometry
• On the ${\Delta }_a$ invariants in non-perturbative complex Chern-Simons theory