The symmetric orbifold of N = 2 $$ \mathcal{N}=2 $$ minimal models

Abstract

The large level limit of the N = 2 minimal models that appear in the duality with the N = 2 supersymmetric higher spin theory on AdS 3 is shown to be a natural subsector of a certain symmetric orbifold theory. We study the relevant decompositions in both the untwisted and the twisted sector, and analyse the structure of the higher spin representations in the twisted sector in some detail. These results should help to identify the string background of which the higher spin theory is expected to describe the leading Regge trajectory in the tensionless limit.

$\mathcal{N}=2$ minimal models: A holographic needle in a symmetric orbifold haystack

“…The study of minimal models has appeared in other contexts in holography; see for instance[25][26][27][28][29][30].…”

Twisted sectors from plane partitions

“…The roots in (A.15) appear already at level 2, while those in (A. 15) and (A.16) appear at level 3; these roots therefore each have higher multiplicity. 9 The new roots (that appear with multiplicity one) are therefore associated to the solutions in (A.17) and (A.18).…”

“…More specifically, 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 also [13,14] for related discussions. On the other hand, it has been more difficult to characterize the twisted sector of the symmetric orbifold from a higher spin perspective -see however [12,15,16] for first steps in this direction. This is an important problem if we want to use the higher spin perspective for the description of string theory at its highly symmetrical tensionless point.…”

Correlation functions in the D1-D5 orbifold CFT

“…There has recently been considerable progress on this subject, see [78][79][80][81], with the holographic duals being conjectured to be symmetric orbifolds of minimal models. The supergravity spectrum was computed in detail in [79], to match with the dual SCFT.…”