Galois Transformations for 3d Quantum Topological Field Theories

3d TQFTs from Argyres-Douglas theories

We construct a new class of three-dimensional topological quantum field theories (3d tqfts) by considering generalized generalized argyres-douglas theories on with a non-trivial holonomy of a discrete global symmetry along the 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.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 theory.We test our proposal by applying localization techniques to the conjectural local descriptions of the and theories.