The Higher Spin Rectangle

TL;DR

This paper introduces the higher spin rectangle algebra, a new algebraic structure related to higher spin theories, which may serve as an intermediate framework between Vasiliev higher spin theory and string theory.

Contribution

It defines the higher spin rectangle algebra from symmetrized bosons and explores its relation to the higher spin square algebra, suggesting a potential link to bulk theories.

Findings

Introduction of the higher spin rectangle algebra

Relation established between the rectangle and square algebras

Implication for interpolating bulk theories

Abstract

The chiral algebra of the symmetric product orbifold of a single-boson CFT corresponds to a "higher spin square" algebra in the large $N$ limit. In this note, we show that a symmetrized collection of $N$ bosons defines a similar structure that we refer to as the higher spin rectangle algebra. We explore the relation of this algebra to the higher spin square algebra. The existence of such a truncated algebra hints at bulk theories interpolating between Vasiliev higher spin theory and string theory.