相关论文: On examples of intermediate subfactors from confor…

In this paper we give a general family of conformal invariants associated to bordered Riemann surfaces endowed with boundary parametrizations, or equivalently compact surfaces endowed with conformal maps. Each invariant is specified by a…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

We compute the Chern subgroup of the 4-th integral cohomology group of a certain classifying space and show that it is a proper subgroup. Such a classifying space gives us new counterexamples for the integral Hodge and Tate conjectures…

This is Part I of a series of papers constructing intertwining operator superalgebras and vertex tensor categories associated to the superconformal minimal models and other related models. In this paper, we construct the intertwining…

New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We…

We present more planar algebraic construction of subfactors than those of Guionet-Jones-Shlyakhtenko-Walker and Kodiyalam-Sunder which start from a subfactor planar algebra and give in a direct way a subfactor of the same standard invariant…

A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ models are studied. The invariants are related to the invariants…

In this paper we define two infinite families of graphs called C-$\delta$ graphs and $\delta$- graph and prove that $\delta$-graphs satisfy $\delta$ conjecture. Also we introduce a family of C-$\delta$ graphs from which we can identify…

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…

We revisit the line of non-unitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension.…

We consider the Wilson line networks of the Chern-Simons $3d$ gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus $2d$ CFT. After general discussion that…

Some facts about von Neumann algebras and finite index inclusions of factors are viewed in the context of local quantum field theory. The possibility of local fields intertwining superselection sectors with braid group statistics is…

We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…

Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…

We develop an elementary divisor theory for the unimodular and the modular group over quadratic field extensions and quaternion algebras. In particular, we investigate which sets of elementary divisors can occur. Under an additional…

Let \( A \subset M \) be an inclusion of von Neumann algebras equipped with a faithful normal semifinite operator valued weight \( E \colon M \to A \). We prove that every positive element \( x \in M \) with \( E(x) < \infty \) satisfies…

This is the first paper of a three-part series in which we develop a theory of conformal blocks for $C_2$-cofinite vertex operator algebras (VOAs) that are not necessarily rational. The ultimate goal of this series is to prove a…

This is the fifth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part V), we study products and iterates…

We derive extrinsic GJMS operators and $Q$-curvatures associated to a submanifold of a conformal manifold. The operators are conformally covariant scalar differential operators on the submanifold with leading part a power of the Laplacian…