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 flow. We prove the coset identification for the N = 2 super- Virasoro nets with c < 3, a key result whose equivalent in the vertex algebra context has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.

Carpi, S., Hillier, R., Kawahigashi, Y., Longo, R., Xu, F. (2015). N=2 Superconformal Nets. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 336, 1285-1328 [10.1007/s00220-014-2234-3].

N=2 Superconformal Nets

Carpi, S;LONGO, ROBERTO;
2015-01-01

Abstract

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 flow. We prove the coset identification for the N = 2 super- Virasoro nets with c < 3, a key result whose equivalent in the vertex algebra context has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.
2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - FISICA MATEMATICA
English
Conformal Field Theory, Operator Algebras
Carpi, S., Hillier, R., Kawahigashi, Y., Longo, R., Xu, F. (2015). N=2 Superconformal Nets. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 336, 1285-1328 [10.1007/s00220-014-2234-3].
Carpi, S; Hillier, R; Kawahigashi, Y; Longo, R; Xu, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/113574
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