3d TQFTs from Argyres-Douglas theories

Abstract

We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1\times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern-Simons and Rozansky-Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the $(G_2{)}_1$ and $(F_4{)}_1$ Chern-Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d $\mathcal{N}=2$ theory. We test our proposal by applying localization techniques to the conjectural $\mathcal{N}=1$ UV Lagrangian descriptions of the $(A_1,A_2)$, $(A_1,A_3)$ and $(A_1,D_3)$ theories.

arXiv comment6 pages

References in corpus (20)

• Infinite Chiral Symmetry in Four Dimensions
• New N=2 Superconformal Field Theories in Four Dimensions
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Vertex operator algebras, Higgs branches, and modular differential equations
• N=1 Deformations and RG Flows of N=2 SCFTs
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• Wild Quiver Gauge Theories
• Fivebranes and 3-manifold homology
• Lagrangians for generalized Argyres-Douglas theories
• Supersymmetric gauge theories with decoupled operators and chiral ring stability
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Chiral algebra of Argyres-Douglas theory from M5 brane
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• More Three Dimensional Mirror Pairs
• Studying superconformal symmetry enhancement through indices
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Holonomy Saddles and Supersymmetry
• Highest weights for truncated shifted Yangians and product monomial crystals
• W-algebras for Argyres-Douglas theories

Cited by in corpus (12)

• Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Rationality and Fusion Rules of Exceptional W-Algebras
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• $\hat{Z}$ invariants at rational $\tau$
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• 3D-3D Correspondence from Seifert Fibering Operators
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras