# N =2 Superconformal Nets

@article{Carpi2012NS, title={N =2 Superconformal Nets}, author={Sebastiano Carpi and Robin Hillier and Yasuyuki Kawahigashi and Roberto Longo and Fengjun Xu}, journal={Communications in Mathematical Physics}, year={2012}, volume={336}, pages={1285-1328} }

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. There are naturally associated nets of spectral triples and the JLO cocycles separate the Ramond sectors. We construct the N = 2 superconformal nets of von Neumann algebras in general, classify them in the discrete series c < 3, and we define and study an operator algebraic version of the N = 2 spectral…

## 18 Citations

### Superconformal nets and noncommutative geometry

- Mathematics
- 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…

### N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of xd

- Mathematics
- 2014

We establish an action of the representations of N = 2-superconformal symmetry on the category of matrix factorisations of the potentials xd and xd−yd, for d odd. More precisely we prove a tensor…

### N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of xd

- MathematicsCommunications in Mathematical Physics
- 2018

We establish an action of the representations of N = 2-superconformal symmetry on the category of matrix factorisations of the potentials xd and xd−yd, for d odd. More precisely we prove a tensor…

### Loop groups and noncommutative geometry

- Mathematics
- 2015

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 level l projective…

### Operator algebras and vertex operator algebras

- Mathematics
- 2017

The study of conformal eld theory (CFT) in two space-time dimensions has found applications to dierent areas of physics and mathematics such as string theory, critical phenomena, innite dimensional…

### Landau-Ginzburg/Conformal Field Theory Correspondence for $x^d$ and Module Tensor Categories

- Mathematics
- 2022

The Landau-Ginzburg/Conformal Field Theory correspondence predicts tensor equivalences between categories of matrix factorisations of certain polynomials and categories associated to the N = 2…

### Haploid algebras in $C^*$-tensor categories and the Schellekens list

- Mathematics
- 2022

. We prove that a haploid associative algebra in a C ∗ -tensor category C is equivalent to a Q-system (a special C ∗ -Frobenius algebra) in C if and only if it is rigid. This allows us to prove the…

### Super-KMS Functionals for Graded-Local Conformal Nets

- Mathematics
- 2015

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over $${\mathbb{R}}$$R with superderivations, roughly speaking…

### CONFORMAL FIELD THEORY, VERTEX OPERATOR ALGEBRAS AND OPERATOR ALGEBRAS

- MathematicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

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 aspects and…

### Conformal field theory, tensor categories and operator algebras

- Mathematics
- 2015

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 algebras are emphasized.…

## References

SHOWING 1-10 OF 64 REFERENCES

### Structure and Classification of Superconformal Nets

- Mathematics
- 2008

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…

### Superconformal nets and noncommutative geometry

- Mathematics
- 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…

### Explicit construction of unitary representations of the N = 2 superconformal algebra

- Physics, Mathematics
- 1986

### Operator algebras and conformal field theory

- Mathematics
- 1993

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very…

### Operator Algebras and Conformal Field Theory

- Mathematics
- 1993

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very…

### On the Representation Theory of Virasoro Nets

- Mathematics
- 2004

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…

### Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification

- Mathematics
- 1986

### Unitarity of rationalN = 2 superconformal theories

- Mathematics
- 1997

We demonstrate that all rational models of theN = 2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu’s algebraA(H0) (for which we give a…