NDLI: On the Jones Index Values for Conformal Subnets

Content Provider	Springer Nature Link
Author	Kawahigashi, Yasuyuki Longo, Roberto Carpi, Sebastia
Copyright Year	2010
Abstract	We consider the smallest values taken by the Jones index for an inclusion of local conformal nets of von Neumann algebras on S $^{1}$ and show that these values are quite more restricted than for an arbitrary inclusion of factors. Below 4, the only non-integer admissible value is 4 cos$^{2}$ π/10, which is known to be attained by a certain coset model. Then no index value is possible in the interval between 4 and $${3 +\sqrt{3}}$$ . The proof of this result is based on α-induction arguments. In the case of values below 4 we also give a second proof of the result. In the course of the latter proof we classify all possible unitary braiding symmetries on the ADE tensor categories, namely the ones associated with the even vertices of the A $_{n}$, D $_{2n }$, E $_{6}$, E $_{8}$ Dynkin diagrams.
Ending Page	108
Page Count	10
Starting Page	99
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	2
Volume Number	92
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-03-31
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Two-dimensional field theories, conformal field theories, etc. Geometry Subfactors and their classification Applications of selfadjoint operator algebras to physics Theoretical, Mathematical and Computational Physics Conformal nets Group Theory and Generalizations Axiomatic quantum field theory; operator algebras Statistical Physics, Dynamical Systems and Complexity Jones index
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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