Engineering topics
Dedushenko, Mykola
Publications and source records attributed to Dedushenko, Mykola.
3d TQFTs from Argyres–Douglas theories
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S 1 × 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 ${\left({G}_{2}\right)}_{1}$ and ${\left({F}_{4}\right)}_{1}$ 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. Finally, 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.
Chiral algebra, localization, modularity, surface defects, and all that
We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.