Conical defects and N=2 higher spin holography

TL;DR

This paper explores conical geometries with maximal fermionic symmetry in N=2 higher spin supergravity and establishes a duality with the N=(2,2) CP^N Kazama-Suzuki model, linking geometries to CFT primary states.

Contribution

It constructs explicit geometric solutions for primary states in the dual CFT and verifies the duality through charge comparisons and null vector relations.

Findings

Mapped conical geometries to CFT primary states.

Constructed solutions for RR-sector primary states.

Confirmed duality via charge and symmetry analysis.

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.