3d Modularity

Abstract

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.

arXiv comment119 pages, 10 figures and 20 tables

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Cited by in corpus (36)

• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• A slow review of the AGT correspondence
• M-theoretic Genesis of Topological Phases
• $\hat{Z}$ at large $N$: from curve counts to quantum modularity
• 3d-3d correspondence for mapping tori
• Quivers for 3-manifolds: the correspondence, BPS states, and 3d $\mathcal{N}$=2 theories
• Higher depth quantum modular forms and plumbed $3$-manifolds
• Higher rank $\hat{Z}$ and $F_K$
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• Cobordism invariants from BPS q-series
• Quantum modularity of partial theta series with periodic coefficients
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• APS $\eta$-invariant, path integrals, and mock modularity
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Seiberg-like dualities for orthogonal and symplectic 3d $\mathcal{N}=2$ gauge theories with boundaries
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Resurgent Analysis for Some 3-manifold Invariants
• Three-Manifold Quantum Invariants and Mock Theta Functions
• Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $\Sigma (2,3,6n+5)$
• Learning BPS Spectra and the Gap Conjecture
• Mock modularity at work, or black holes in a forest
• Mahler Measure for a Quiver Symphony
• Quantum Modular $\hat{Z}{}^G$-Invariants
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• 3D-3D Correspondence from Seifert Fibering Operators
• Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs
• Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary
• Orientation Reversal and the Chern-Simons Natural Boundary
• Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums
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• Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves
• $c_{\mathrm{eff}}$ from Resurgence at the Stokes Line
• Generalized theta series and monodromy of Casimir connection. The case of rank 1
• On the ${\Delta }_a$ invariants in non-perturbative complex Chern-Simons theory
• A supergroup series for knot complements