Twisted sectors from plane partitions

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 ∞ 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.

The supersymmetric affine Yangian

“…Obviously, U 0 commutes with all e r , f r ,ê r andf r generators, and because of the relations we have imposed, it also commutes with the x s andx s generators. We also know that the total Möbius generators correspond to 33) and it is thus natural to assume that the ±1 modes of the decoupled boson are…”

“…The main technical difficulty of this approach comes from the fact that the description of conjugate minimal representations in terms of the affine Yangian was not known. The affine Yangian viewpoint gives rise to an elegant description of representations in terms of plane partitions [19], see also [33], but this language only applies to the "box"-representations, but not to those made of "anti-boxes". However, the bi-minimal representations that are relevant for the above extension always involve also anti-box representations.…”

Higher spins and Yangian symmetries

“…three-dimensional box stacking configurations. 3 They are special in that they have a finite number of states at every level and thus possess infinitely many null states; they are discussed in some detail in [11,25], and we only summarize the salient aspects which we will draw upon later. A generic plane partition representation is labelled by three Young tableaux.…”

“…One advantage of the plane partition viewpoint in describing representations of W ∞ , even those of the coset type, is that it is much easier to compute the character via the combinatorics of box stacking than using the Kac-Weyl character formula. For example, this idea was used to identify the twisted sector representations of the symmetric orbifold in [25].…”

Quantizing higher-spin gravity in free-field variables

“…The same states have been also recently considered in a related holographic scenario, where they have been identified in the twisted sector of symmetric orbifold CFT's, which have been conjectured to be dual to the tensionless limit of strings on AdS3[16].…”