Spectral triples and the super-Virasoro algebra

Abstract

We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representation of the Ramond algebra with central charge c and minimal lowest weight h=c/24 is graded and gives rise to a net of even theta-summable spectral triples with non-zero Fredholm index. The irreducible unitary positive energy representations of the Neveu-Schwarz algebra give rise to nets of even theta-summable generalised spectral triples where there is no Dirac operator but only a superderivation.

27 pages; v2: a comment concerning the difficulty in defining cyclic cocycles in the NS case have been added

References in corpus (2)

• Structure and Classification of Superconformal Nets
• Algebraic Supersymmetry: A case study

Cited by in corpus (15)

• Conformal Field Theory, Tensor Categories and Operator Algebras
• Representations of Conformal Nets, Universal C*-Algebras and K-Theory
• N=2 superconformal nets
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• Local energy bounds and strong locality in chiral CFT
• Compact $\kappa$-deformation and spectral triples
• $\kappa$-Deformation and Spectral Triples
• The C(X)-algebra of a net and index theory
• Energy bounds for vertex operator algebra extensions
• The K-homology of nets of C*-algebras
• Super-KMS functionals for graded-local conformal nets
• From Operator Algebras to Superconformal Field Theory
• Local-entire cyclic cocycles for graded quantum field nets
• From vertex operator superalgebras to graded-local conformal nets and back
• Loop groups and noncommutative geometry