Limits of minimal models and continuous orbifolds

TL;DR

This paper explores the limits of 2d minimal models, showing their relation to free boson theories and continuous orbifolds, and discusses how adding twisted sectors can restore consistency and crossing symmetry.

Contribution

It demonstrates that the lambda=0 't Hooft limit of 2d W_N minimal models corresponds to a continuous orbifold, and clarifies the role of twisted sectors in ensuring consistency.

Findings

The lambda=0 limit is equivalent to the singlet sector of a free boson theory.

Twisted sectors restore modular invariance and include light states.

The construction satisfies crossing symmetry and matches known limit theories.

Abstract

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.