Superconformal nets and noncommutative geometry

@article{Carpi2013SuperconformalNA,
  title={Superconformal nets and noncommutative geometry},
  author={Sebastiano Carpi and Robin Hillier and Roberto Longo},
  journal={arXiv: Operator Algebras},
  year={2013}
}
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 Delta of localized endomorphisms of the even part A^gamma of A, we define the locally convex differentiable algebra A_Delta with respect to a natural Dirac operator coming from supersymmetry. Having determined its structure and properties, we study the family of spectral triples and JLO entire cyclic cocycles associated… 
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References

SHOWING 1-10 OF 69 REFERENCES
Structure and Classification of Superconformal Nets
Abstract.We study the general structure of Fermi conformal nets of von Neumann algebras on S1 and consider a class of topological representations, the general representations, that we characterize as
N =2 Superconformal Nets
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 much richer.
Noncommutative Geometry
Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In
Kac-Moody and Virasoro algebras
These are the notes for a Part III course given in the University of Cambridge in autumn 1998. They contain an exposition of the representation theory of the Lie algebras of compact matrix groups,
Multi-Interval Subfactors and Modularity¶of Representations in Conformal Field Theory
Abstract: We describe the structure of the inclusions of factors ?(E)⊂?(E′)′ associated with multi-intervals E⊂ℝ for a local irreducible net ? of von Neumann algebras on the real line satisfying the
Superconformal current algebras and their unitary representations
A natural supersymmetric extension (dG)κ is defined of the current (= affine Kac-Moody Lie) algebra dG; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory
On the Representation Theory of Virasoro Nets
We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro
Twisted cyclic theory, equivariant KK-theory and KMS states
Abstract Given a C*-algebra A with a KMS weight for a circle action, we construct and compute a secondary invariant on the equivariant K-theory of the mapping cone of , both in terms of equivariant
Modular structure and duality in conformal quantum field theory
Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with
Algebraic Supersymmetry: A Case Study
The treatment of supersymmetry is known to cause difficulties in the C*–algebraic framework of relativistic quantum field theory; several no–go theorems indicate that super–derivations and super–KMS
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