Abstract
Twisted sectors arise naturally in the bosonic higher spin CFTs at their free points, as well as in the associated symmetric orbifolds. We identify the coset representations of the twisted sector states using the description of W_\infty representations in terms of plane partitions. We confirm these proposals by a microscopic null-vector analysis, and by matching the excitation spectrum of these representations with the orbifold prediction.
Highlights
Orbifold of T4, and the orbifold theory itself contains a vector-like CFT as a closed subsector
The CFT dual of the higher spin theory is a subsector of the untwisted sector of the symmetric orbifold, and the entire untwisted sector can be understood in terms of a vastly extended higher spin symmetry, the so-called Higher Spin Square (HSS), as well as its scalar field excitations [11, 12], see [13, 14] for related discussions
A few years ago it was shown in a series of papers [18,19,20] that the representation theory of the quantum toroidal algebra of gl1 can be described in terms of plane partitions, and that the associated characters are, up to an overall qPochhammer symbol, identical to those of the bosonic WN,k minimal models
Summary
We shall mainly be considering the ’t Hooft limit, where we take N and k to infinity, while keeping the ratio. The theory should contain twisted sectors where the different complex bosons are twisted, and these twisted sectors are representations of W∞[1]. We will first focus on the case of a continuous orbifold twist where only one complex boson is twisted by an arbitrary ν ∈ [0, 1) (with all remaining k − 1 bosons untwisted). We will tensor multiple bosons together to form more generic twisted sector states of the continuous orbifold, and thereby describe those of the symmetric orbifold. In the full orbifold theory, this chiral representation comes together with a corresponding anti-chiral representation, and on the full space (involving both chiral and anti-chiral twisted states) the invariance under the orbifold group is to be imposed.
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