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Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…

Quantum Algebra · Mathematics 2016-10-18 Chongying Dong , Li Ren

We show that a braided monoidal category C can be endowed with the structure of a right (and left) module category over C \times C. In fact, there is a family of such module category structures, and they are mutually isomorphic if and only…

Category Theory · Mathematics 2010-02-05 Till Barmeier , Jurgen Fuchs , Ingo Runkel , Christoph Schweigert

We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with…

High Energy Physics - Theory · Physics 2008-11-26 Jürg Fröhlich , Jürgen Fuchs , Ingo Runkel , Christoph Schweigert

The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling $N$…

Statistical Mechanics · Physics 2024-12-30 Yang Ge , Shao-Kai Jian

We use the F-theory realization of 6D superconformal field theories (SCFTs) to study the corresponding spectrum of stringlike, i.e. surface defects. On the tensor branch, all of the stringlike excitations pick up a finite tension, and there…

High Energy Physics - Theory · Physics 2016-05-25 Michele Del Zotto , Jonathan J. Heckman , Daniel S. Park , Tom Rudelius

This article gives a solid theoretical grounding to the observation that cubical structures arise naturally when working with parametricity. We claim that cubical models are cofreely parametric. We use categories, lex categories or clans as…

Logic in Computer Science · Computer Science 2022-09-05 Hugo Moeneclaey

In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal…

High Energy Physics - Theory · Physics 2022-07-26 Dimosthenis Theofilopoulos

The two pillars of rational conformal field theory and rational vertex operator algebras are modularity of characters on the one hand and its interpretation of modules as objects in a modular tensor category on the other one. Overarching…

Quantum Algebra · Mathematics 2017-10-11 Thomas Creutzig , Terry Gannon

We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…

Disordered Systems and Neural Networks · Physics 2015-06-25 V. Gurarie , A. W. W. Ludwig

Given an arbitrary countably generated rigid C*-tensor category, we construct a fully-faithful bi-involutive strong monoidal functor onto a subcategory of finitely generated projective bimodules over a simple, exact, separable, unital…

Operator Algebras · Mathematics 2026-01-06 Michael Hartglass , Roberto Hernandez Palomares

Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS…

High Energy Physics - Theory · Physics 2026-02-03 Davide Gaiotto , Nikita Grygoryev , Wei Li

Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action. Then we can define a right $A$-action…

Category Theory · Mathematics 2010-11-23 D. Bulacu , S. Caenepeel

The continuation of the Liouville conformal field theory to c<=1 is considered. The viability of an interpretation involving a timelike boson which is the conformal factor for two-dimensional asymptotically de Sitter geometries is examined.…

High Energy Physics - Theory · Physics 2008-11-26 Will McElgin

Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches…

Mathematical Physics · Physics 2024-11-20 Bolin Han

It has long been known that every weak monoidal category A is equivalent via monoidal functors and monoidal natural transformations to a strict monoidal category st(A). We generalise the definition of weak monoidal category to give a…

Category Theory · Mathematics 2007-05-23 Miles Gould

We study generalized symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. This paper follows our companion paper on gapped phases and anomalies associated with these symmetries. In the present…

High Energy Physics - Theory · Physics 2021-06-25 Ryan Thorngren , Yifan Wang

We develop the theory of module categories over a Grothendieck-Verdier category, i.e. a monoidal category with a dualizing object and hence a duality structure more general than rigidity. Such a category C comes with two monoidal structures…

Category Theory · Mathematics 2024-06-03 Jürgen Fuchs , Gregor Schaumann , Christoph Schweigert , Simon Wood

We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…

Algebraic Topology · Mathematics 2010-10-12 Arthur Bartels , Christopher L. Douglas , André G. Henriques

Conformal field theory (CFT) in two dimensions provide a rich source of subfactors. The fact that there are so many subfactors coming from CFT have led people to conjecture that perhaps all finite depth subfactors are related to CFT. In…

Operator Algebras · Mathematics 2017-08-02 Feng Xu

The presence of a boundary (or defect) in a conformal field theory allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of protected scaling dimension $\Delta$ equal to the…

High Energy Physics - Theory · Physics 2020-02-19 Christopher P. Herzog , Itamar Shamir