Dimensional Reduction, Extended Topological Field Theories and Orbifoldization

Extended Homotopy Quantum Field Theories and their Orbifoldization

We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological field theories. More precisely, we use a bicategorical version of the parallel section functor to associate to an extended equivariant topological field theory an ordinary extended topological field theory. Thereby, we give a unification, geometric underpinning and vast generalization of algebraic concepts of orbifoldization. In the special case of 3-2-1-dime…

Orbifold Construction for Topological Field Theories

An equivariant topological field theory is defined on a cobordism category of manifolds with principal fiber bundles for a fixed (finite) structure group. We provide a geometric construction which for any given morphism $G \to H$ of finite groups assigns in a functorial way to a $G$-equivariant topological field theory an $H$-equivariant topological field theory, the pushforward theory. When $H$ is the trivial group, this yields an orbifold construction for $G$-equivariant topological field theories which unifies and generalizes several known algebraic notions of orbifoldization.

(A₂,D_{3n−2}) Argyres–Douglas理论的SCFT/VOA对应与R-扭曲约化

SCFT/VOA correspondence and R-twisted reductions of $(A_2,D_{3n-2})$ Argyres--Douglas theories

本文研究n≥2时(A₂,D_{3n−2}) Argyres–Douglas理论的SCFT/VOA对应，提出相关VOA为对数二重态代数𝒜(4n−2)，推广n=2的结果并构造对应3d理论，验证其超对称与分支结构。