Bicategories in field theories - an invitation

An invitation to loop quantum gravity

We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicsts in other areas such as string theory, cosmology, particle physics, astrophysics and condensed matter physics. No details are given, but references are provided to guide the interested reader to the literature. The present state of knowledge is summarized in a list of 35 key results on topics including the hamiltonian and path integral…

Bicategories for boundary conditions and for surface defects in 3-d TFT

We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation b…

SAGEX散射振幅综述，第2章：色-运动学对偶与双重拷贝导论

The SAGEX Review on Scattering Amplitudes, Chapter 2: An Invitation to Color-Kinematics Duality and the Double Copy

本文综述色-运动学对偶与双重拷贝结构，介绍其在规范、引力及有效场论中的表现，并展示可构造理论网络与引力波计算应用。

Orbifold completion of defect bicategories

Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of defects or domain walls. This perspective allows for a rich generalisation of the orbifolding procedure, which we study in detail for the case of topological field theories. Namely, a TFT with defects gives rise to a pivotal bicategory of "worldsheet phases" and defects between them. We develop a general framework which takes such a bicategory B as input and returns its "orbifold completion" B_orb. The completion satisfies the natural properties B \subset B_orb and (B_orb)_orb = B_orb, and it gives rise …

An invitation to Poisson-Lie T-duality in Double Field Theory and its applications

Poisson-Lie (PL) T-duality has received much attention over the last five years in connection with integrable string worldsheet theories. At the level of the worldsheet, the algebraic structure underpinning these connections is made manifest with the $\mathcal{E}$-model, a first order Hamiltonian description of the string. The $\mathcal{E}$-model shares many similarities with Double Field Theory (DFT). We report on recent progress in establishing a precise linkage with DFT as the target space description of the $\mathcal{E}$-model. There are three important outcomes of this endeavor: 1) PL sym…

论量子场论中拓扑缺陷的高阶范畴结构

On the Higher Categorical Structure of Topological Defects in Quantum Field Theories

本文提出一个基于结构化高阶dagger范畴的统一数学框架，用于描述量子场论中带切向结构的拓扑缺陷的高阶范畴结构，并在分层配边假设下对具有稳定切向结构且允许直和的情形给出了证明。