Defect lines, dualities, and generalised orbifolds

Constructing modular categories from orbifold data

In Carqueville et al., arXiv:1809.01483, the notion of an orbifold datum $\mathbb{A}$ in a modular fusion category $\mathcal{C}$ was introduced as part of a generalised orbifold construction for Reshetikhin-Turaev TQFTs. In this paper, given a simple orbifold datum $\mathbb{A}$ in $\mathcal{C}$, we introduce a ribbon category $\mathcal{C}_{\mathbb{A}}$ and show that it is again a modular fusion category. The definition of $\mathcal{C}_{\mathbb{A}}$ is motivated by properties of Wilson lines in the generalised orbifold. We analyse two examples in detail: (i) when $\mathbb{A}$ is given by a simp…

A quick guide to defect orbifolds

We provide a lightning review of the construction of (generalised) orbifolds [arXiv:0909.5013, arXiv:1210.6363] of two-dimensional quantum field theories in terms of topological defects, along the lines of [arXiv:1307.3141]. This universal perspective has many applications, some of which we sketch in the examples of 2d Yang-Mills theory, Landau-Ginzburg models, and rational CFT.

三维轨形上的超对称与局域化

Supersymmetry and Localization on Three-Dimensional Orbifolds

本文研究三维${\rm N}=2$超对称场论在纺锤体圆周丛背景下的配分函数，提出统一超共形与拓扑扭曲指标的纺锤体指标，并用非微扰对偶验证，还得到二维紧化理论的单圈行列式。

Orbifolds of Reshetikhin-Turaev TQFTs

We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a modular tensor category $\mathcal{C}$, using the language of defect TQFT from [arXiv:1705.06085]: (i) spherical fusion categories give orbifolds for the "trivial" defect TQFT associated to vect, (ii) $G$-crossed extensions of $\mathcal{C}$ give group orbifolds for any finite group $G$, and (iii) we construct orbifolds from commutative $Δ$-separable symmetric Frobenius algebras in $\mathcal{C}$. We also explain how the Turaev-Viro state sum construction fits into our framework by proving that it is isomorphic…

Orbifolds and topological defects

We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau-Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes. Our construction al…

通过Orbifold数据、Zesting和Equivariantisation实现可逆对称性的例子

Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation

本文研究了通过equivariantisation、G-交叉braided zesting和广义orbifold构造实现可逆对称性的方法，特别是在三维情况下，并探讨了这些方法之间的关系以及在不同例子中的应用。

Orbifolds of n-dimensional defect TQFTs

We introduce the notion of $n$-dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension $n$. The familiar closed or open-closed TQFTs are special cases of defect TQFTs, and for $n=2$ and $n=3$ our general definition recovers what had previously been studied in the literature. Our main construction is that of "generalised orbifolds" for any $n$-dimensional defect TQFT: Given a defect TQFT $\mathcal{Z}$, one obtains a new TQFT $\mathcal{Z}_{\mathcal{A}}$ by decorating the Poincaré duals of triangulated bordisms…

Symmetry defects and orbifolds of two-dimensional Yang-Mills theory

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted $G$-bundles, and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted $G$-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, wh…

3范畴的orbifold完成

Orbifold completion of 3-categories

本文提出了一种3范畴的orbifold完成理论，通过构造Morita范畴来描述拓扑量子场论及其缺陷，并展示了其在缺陷TQFT中的应用。