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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
