Related papers: Modular invariants and subfactors
Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the…
The affine $su(3)$ modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II)…
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories…
Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always…
In the framework of algebraic quantum field theory, we study the category \Delta_BF^A of stringlike localised representations of a net of observables O \mapsto A(O) in three dimensions. It is shown that compactly localised (DHR)…
The algebraic notion of a pivotal module category was developed by Schaumann and Shimizu and is central to the description of boundary conditions in conformal field theory according to a proposal by Fuchs and Schweigert. In this paper, we…
We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by an interval when the system is in the ground state, either on the line or on the circle,…
A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\phi: B_k \rightarrow…
In this paper, we give a general axiomatization of anomalies in closed and open conformal field theories. In particular, we generalize Segal's notion of modular functor to a setting where the ``set of labels'' is a 2-vector space. In the…
We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain…
We study the modular symmetry in four-dimensional low-energy effective field theory, which is derived from type IIB magnetized D-brane models and type IIA intersecting D-brane models. We analyze modular symmetric behaviors of perturbative…
By using the notion of a rigid R-matrix in a monoidal category and the Reshetikhin--Turaev functor on the category of tangles, we review the definition of the associated invariant of long knots. In the framework of the monoidal categories…
The deepest arithmetic invariants attached to an algebraic variety defined over a number field $F$ are conjecturally captured by the integral part of its motivic cohomology. There are essentially two ways of defining it when $X$ is a smooth…
We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of…
The tensor functor called $\alpha$-induction arises from a Frobenius algebra object, or a Q-system, in a braided unitary fusion category. In the operator algebraic language, it gives extensions of endomorphism of $N$ to $M$ arising from a…
We define an invariant of tangles and framed tangles given a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying natural properties. We give several examples of Reidemeister pairs derived from racks,…
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…