53 citations · 256 across the 21 of their papers we have counts for
11 papers · 1 filter
From vertex operator superalgebras to graded-local conformal nets and back
Sebastiano Carpi, Tiziano Gaudio, Robin Hillier
We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between vertex operator algebras and conformal nets to the case of vertex operator superalgebras and graded-local co…
Roots of Completely Positive Maps
B. V. Rajarama Bhat, Robin Hillier, Nirupama Mallick +1
We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots an…
Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
Sebastiano Carpi, Tiziano Gaudio, Robin Hillier
We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebr…
Loop groups and noncommutative geometry
Sebastiano Carpi, Robin Hillier
We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the le…
Local-entire cyclic cocycles for graded quantum field nets
Robin Hillier
In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over R, and…
Superconformal nets and noncommutative geometry
Sebastiano Carpi, Robin Hillier, Roberto Longo
This paper provides a further step in our program of studying superconformal nets over S^1 from the point of view of noncommutative geometry. For any such net A and any family Delt…
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…
Conformal nets and KK-theory
Sebastiano Carpi, Roberto Conti, Robin Hillier
Given a completely rational conformal net A on the circle, its fusion ring acts faithfully on the K_0-group of a certain universal C*-algebra associated to A, as shown in a previou…
Super-KMS functionals for graded-local conformal nets
Robin Hillier
Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speak…
Representations of Conformal Nets, Universal C*-Algebras and K-Theory
Sebastiano Carpi, Roberto Conti, Robin Hillier +1
We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal C*-algebra C*(A). We prove that if A satisfies the spli…
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…