225 citations · 1.1k across the 38 of their papers we have counts for
20 papers · 1 filter
A characterization of a finite-dimensional commuting square producing a subfactor of finite depth
Yasuyuki Kawahigashi
We give a characterization of a finite-dimensional commuting square of C*-algebras with a normalized trace that produces a hyperfinite type II_1 subfactor of finite index and finit…
Projector Matrix Product Operators, Anyons and Higher Relative Commutants of Subfactors
Yasuyuki Kawahigashi
A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth gives a 4-tensor appearing in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haeg…
The relative Drinfeld commutant of a fusion category and -induction
Yasuyuki Kawahigashi
We establish a correspondence among simple objects of the relative commutant of a full fusion subcategory in a larger fusion category in the sense of Drinfeld, irreducible half-bra…
A relative tensor product of subfactors over a modular tensor category
Yasuyuki Kawahigashi
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full l…
From vertex operator algebras to conformal nets and back
Sebastiano Carpi, Yasuyuki Kawahigashi, Roberto Longo +1
We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a ge…
Tensor categories and endomorphisms of von Neumann algebras (with applications to Quantum Field Theory)
Marcel Bischoff, Roberto Longo, Yasuyuki Kawahigashi +1
Q-systems describe "extensions" of an infinite von Neumann factor , i.e., finite-index unital inclusions of into another von Neumann algebra . They are (special cases of)…
Normal states of type III factors
Yasuyuki Kawahigashi, Yoshiko Ogata, Erling Størmer
Let M be a factor of type III with separable predual and with normal states phi_1,...,phi_k, omega with omega faithful. Let A be a finite dimensional C*-subalgebra of M. Then it is…
N=2 superconformal nets
Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi +2
We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is mu…
On the Jones index values for conformal subnets
Sebastiano Carpi, Yasuyuki Kawahigashi, Roberto Longo
We consider the smallest values taken by the Jones index for an inclusion of local conformal nets of von Neumann algebras on S^1 and show that these values are quite more restricte…
Spectral triples and the super-Virasoro algebra
Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi +1
We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representat…
The classification of non-local chiral CFT with c<1
Y. Kawahigashi, R. Longo, U. Pennig +1
All non-local but relatively local irreducible extensions of Virasoro chiral CFTs with c<1 are classified. The classification, which is a prerequisite for the classification of loc…
Local conformal nets arising from framed vertex operator algebras
Yasuyuki Kawahigashi, Roberto Longo
We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III_1) factors on the circle corresponding to various lattice verte…
Topological Quantum Field Theories and Operator Algebras
Yasuyuki Kawahigashi
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
Classification of operator algebraic conformal field theories
Yasuyuki Kawahigashi
We give an exposition on the current status of classification of operator algebraic conformal field theories. We explain roles of complete rationality and alpha-induction for nets…
(2+1)-dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3-manifold invariants
Yasuyuki Kawahigashi, Nobuya Sato, Michihisa Wakui
In this paper, we establish the general theory of (2+1)-dimensional topological quantum field theory (in short, TQFT) with a Verlinde basis. It is a consequence that we have a Dehn…
Generalized Longo-Rehren subfactors and alpha-induction
Yasuyuki Kawahigashi
We study the recent construction of subfactors by Rehren which generalizes the Longo-Rehren subfactors. We prove that if we apply this construction to a non-degenerately braided su…
Longo-Rehren subfactors arising from -induction
J. Böckenhauer, D. E. Evans, Y. Kawahigashi
We study (dual) Longo-Rehren subfactors arising from various systems of endomorphisms of M obtained from alpha-induction for some braided subfactor $N\…
Chiral structure of modular invariants for subfactors
J. Böckenhauer, D. E. Evans, Y. Kawahigashi
In this paper we further analyze modular invariants for subfactors, in particular the structure of the chiral induced systems of M-M morphisms. The relative braiding between the ch…
On -induction, chiral generators and modular invariants for subfactors
J. Böckenhauer, D. E. Evans, Y. Kawahigashi
We consider a type III subfactor of finite index with a finite system of braided - morphisms which includes the irreducible constituents of the dual canonical en…
Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
Yasuyuki Kawahigashi, Roberto Longo, Michael Mueger
We describe the structure of the inclusions of factors A(E) contained in A(E')' associated with multi-intervals E of R for a local irreducible net A of von Neumann algebras on the…