The Holographic Dual of a SUSY Vector Model and Tensionless Open Strings

We describe a supersymmetric example of the holographic duality between 3 dimensional vector models and higher spin gauge theories in AdS4, first proposed in a bosonic context by Klebanov and Polyakov. We argue that a particular Fradkin-Vasiliev type supersymmetric higher spin gauge theory in AdS4 with 16 supersymmetries is dual to the singlet sector of bilinear operators of a free N = 4, SU(N) vector model defined on the boundary. Starting from the duality between type IIB on AdS5 × S with a D5–brane as an AdS4×S subspace and the 4 dimensional SU(N) SYM with a defect, we recover the duality between our vector model and the higher spin gauge theory. In this case, we propose that the higher spin gauge theory is a truncation of the open string theory on the world volume of the D5-brane in its tensionless string limit. We also comment on a possible Higgs mechanism in our model.