On matter coupled to the higher spin square

Understand

Gaberdiel and Gopakumar recently proposed that the tensionless limit of string theory on $AdS_3 \times S^3 \times T^4$ takes the form of a higher spin theory with a gauge algebra that is referred to as the higher spin square.

• In this note, we formulate the linearized Vasiliev-type equations which describe a matter field coupled to the higher spin square.
• We study the particle spectrum of this field and show that it accounts for the entire untwisted sector of the dual symmetric orbifold CFT, thereby confirming a conjecture by Gaberdiel and Gopakumar.
• In doing so, we pinpoint the group-theoretic data which determine the spectrum of a matter field coupled to a general higher spin algebra, which we illustrate by revisiting the theory based on the $hs[1/2]$ algebra.