Limits of minimal models and continuous orbifolds

Understand

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.