225 citations · 1.1k across the 38 of their papers we have counts for
15 papers · 1 filter
Subfactors and Mathematical Physics
David E. Evans, Yasuyuki Kawahigashi
This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics,qu…
Two-dimensional topological order and operator algebras
Yasuyuki Kawahigashi
We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of repre…
Conformal Field Theory, Vertex Operator Algebras and Operator Algebras
Yasuyuki Kawahigashi
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 a…
Conformal Field Theory, Tensor Categories and Operator Algebras
Yasuyuki Kawahigashi
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algeb…
Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case
Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo
Let be a completely rational local Möbius covariant net on , which describes a set of chiral observables. We show that local Möbius covariant nets $\mathcal{B}_2…
Phase boundaries in algebraic conformal QFT
Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo +1
We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries…
Construction of holomorphic local conformal framed nets
Yasuyuki Kawahigashi, Noppakhun Suthichitranont
We construct holomorphic local conformal framed nets extended from a tensor power of the Virasoro net with c=1/2 with a pair of binary codes (C,D) satisfying the conditions given b…
How to add a boundary condition
Sebastiano Carpi, Yasuyuki Kawahigashi, Roberto Longo
Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on t…
From Operator Algebras to Superconformal Field Theory
Yasuyuki Kawahigashi
We make a review on the recent progress in the operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boun…
Structure and Classification of Superconformal Nets
Sebastiano Carpi, Yasuyuki Kawahigashi, Roberto Longo
We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we…
Conformal Field Theory and Operator Algebras
Yasuyuki Kawahigashi
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based…
Noncommutative Spectral Invariants and Black Hole Entropy
Yasuyuki Kawahigashi, Roberto Longo
We consider an intrinsic entropy associated with a local conformal net A by the coefficients in the expansion of the logarithm of the trace of the ``heat kernel'' semigroup. In ana…
Classification of operator algebraic conformal field theories in dimensions one and two
Yasuyuki Kawahigashi
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dim…
Classification of Two-dimensional Local Conformal Nets with c<1 and 2-cohomology Vanishing for Tensor Categories
Yasuyuki Kawahigashi, Roberto Longo
We classify two-dimensional local conformal nets with parity symmetry and central charge less than 1, up to isomorphism. The maximal ones are in a bijective correspondence with the…
Classification of Local Conformal Nets. Case c < 1
Yasuyuki Kawahigashi, Roberto Longo
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspond…