On matter coupled to the higher spin square

Abstract

Gaberdiel and Gopakumar recently proposed that the tensionless limit of string theory on $Ad{S}_3\times S^3\times T^4$ 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.

18 pages. V2: minor changes, reference added

References in corpus (8)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Higher Spins & Strings
• Quantum W-symmetry in AdS_3
• The symmetry of large N=4 holography
• Finite higher spin transformations from exponentiation
• Higher spins from Nambu-Chern-Simons theory

Cited by in corpus (4)

• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Simple Unfolded Equations for Massive Higher Spins in AdS${}_3$
• On tensionless string field theory in AdS${}_3$