A note on conical solutions in 3D Vasiliev theory

TL;DR

This paper constructs smooth conical solutions in 3D Vasiliev higher spin theories with hs[c6] algebra, generalizing known solutions and linking them to specific primary states of the W_[c6] algebra in a classical limit.

Contribution

It introduces a new class of smooth solutions in Vasiliev higher spin theories that generalize previous conical defect solutions and connect to algebraic structures in a specific classical limit.

Findings

Solutions reduce to known sl(N) conical defects when c6=N.

Evidence links these solutions to primary states of W_[c6] algebra.

The solutions are relevant in the Gaberdiel-Gopakumar-'t Hooft limit with large c6.

Abstract

We construct a class of smooth solutions in three-dimensional Vasiliev higher spin theories based on the gauge algebra hs[\lambda]. These solutions naturally generalize the previously constructed conical defect solutions in higher spin theories with sl(N) gauge algebra, to which they reduce when \lambda is taken to be equal to N. We provide evidence for their identification with specific primary states of the W_\infty [\lambda] algebra in a particular classical limit. In terms of the Gaberdiel-Gopakumar-'t Hooft limit of the W_N minimal models, this limit corresponds to a regime where the 't Hooft coupling becomes large.