Conical defects and N=2 higher spin holography

TL;DR

This work advances ${\cal N}=2$ higher spin holography by analyzing conical defects in ${\rm sl}(N+1|N)\oplus{\rm sl}(N+1|N)$ Chern-Simons supergravity that preserve maximal fermionic symmetry. It shows how these bulk geometries, when enhanced to smooth configurations, are labeled by two Young diagrams and a ${\rm u}(1)$ charge, and maps them to primary states of the ${\cal N}=2$ ${\rm W}_{N+1}$-symmetric ${\rm CP}^N$ Kazama-Suzuki model in the large central charge limit, distinguishing NSNS and RR sectors. The authors compare bulk and boundary charges, relate null vectors to residual higher-spin symmetries, and discuss one-loop gravity partition functions derived from the CFT null-vector structure. The results bolster a precise bulk/boundary dictionary in this supersymmetric, higher-spin context and point to interesting avenues for exploring $1/$central-charge corrections, unitarity, and black-hole solutions within ${\cal N}=2$ higher spin holography.

Abstract

We study conical geometry with the maximal number of fermionic symmetry in the higher spin supergravity described by sl(N+1|N) + sl(N+1|N) Chern-Simons gauge theory. It was proposed that a three dimensional N=2 higher spin supergravity is holographically dual to the N=(2,2) CP^N Kazama-Suzuki model. Based one the duality, we find a map between conical geometries and primary states in the dual CFT. In particular, we construct geometric solutions corresponding to primary states in the RR-sector. The proposal is checked by the comparison of a few charges and by the relation between null vectors and higher spin symmetry.