3d TQFTs from ArgyresDouglas theories
Abstract
We construct a new class of threedimensional topological quantum field theories (3d TQFTs) by considering generalized ArgyresDouglas theories on $S^1 \times M_3$ with a nontrivial holonomy of a discrete global symmetry along the $S^1$. For the minimal choice of the holonomy, the resulting 3d TQFTs are nonunitary and semisimple, thus distinguishing themselves from theories of ChernSimons and RozanskyWitten 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 $(F_4)_1$ ChernSimons 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 DOI:
 10.48550/arXiv.1809.04638
 arXiv:
 arXiv:1809.04638
 Bibcode:
 2018arXiv180904638D
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 6 pages