Related papers: Modular functors and CFT correlators via double ca…
Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category. An essential ingredient in our construction is a graphical…
This lecture series is based on joint work in progress with Shaul Barkan, as well as work in progress of the author. The five sections of these notes correspond to the five lectures, but more details have been added. $2$-dimensional…
We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories.…
We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations. The modular functor is defined on bordisms that are 2-framed. Accordingly we do not need…
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…
Let $R$ be an associative ring with unit. Given an $R$-module $M$, we can associate the following covariant functor from the category of $R$-algebras to the category of abelian groups: $S\mapsto M\otimes_R S$. With the corresponding notion…
The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module category are given by internal Homs and coHoms, respectively. We…
To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule…
We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is then defined as a certain…
Conformal nets provides a mathematical model for conformal field theory. We define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. We introduce an operation of fusion…
The bicategorical point of view provides a natural setting for many concepts in the representation theory of monoidal categories. We show that centers of twisted bimodule categories correspond to categories of 2-dimensional natural…
The category of double categories and double functors is equipped with a symmetric closed monoidal structure. For any double category $\mathbb A$, the corresponding internal hom functor $|[ \mathbb A,-]|$ sends a double category $\mathbb B$…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…
We call a tensor functor $F:\mathcal{C}\to\mathcal{D}$ between finite tensor categories $\otimes$-Frobenius if its left and right adjoints are isomorphic as $\mathcal{C}$-bimodule functors. We give several characterizations of this notion…
We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these types of 2-dimensional extended topological…
We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…