Limits of minimal models and continuous orbifolds

Details Limits of minimal models and continuous orbifolds Limits of minimal models and continuous orbifolds

2011-12-07

arxiv.org/abs/1112.1708v2

JHEP 1203:104,2012

Physics

High Energy Physics

High Energy Physics - Theory

33 pages; v2: minor improvements and references added, published version

Scientific paper

10.1007/JHEP03(2012)104

The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the `light states' that were not included in the original 't Hooft limit. We also show that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.

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