TY - JOUR

T1 - N = 2 superconformal nets

AU - Carpi, Sebastiano

AU - Hillier, Robin

AU - Kawahigashi, Yasuyuki

AU - Longo, Roberto

AU - Xu, Feng

PY - 2015/6

Y1 - 2015/6

N2 - 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 study 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 is seemingly not complete. Finally, the chiral ring is discussed in terms of net representations.

AB - 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 study 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 is seemingly not complete. Finally, the chiral ring is discussed in terms of net representations.

U2 - 10.1007/s00220-014-2234-3

DO - 10.1007/s00220-014-2234-3

M3 - Journal article

VL - 336

SP - 1285

EP - 1328

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -