Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual

TL;DR

The work analyzes Vasiliev's higher-spin gravity in AdS_3 coupled to massive scalars and tests a refined AdS/CFT duality to a subsector of the W_N minimal model. By constructing boundary-to-bulk propagators under proper higher-spin boundary conditions and computing tree-level two- and three-point functions, the authors find nontrivial agreement with the large-N coset CFT at specific 't Hooft values, notably λ=1/2. They propose that the bulk theory is perturbatively complete within a closed subsector generated by two basic primaries, with a minimal truncation to even spins mapping to an SO(N) coset analog; nonperturbative completeness and extension to the full W_N model remain open. The results provide concrete, calculable tests of higher-spin holography in AdS_3 and yield precise predictions for higher-spin correlators in the CFT subsector.

Abstract

We study Vasiliev's system of higher spin gauge fields coupled to massive scalars in AdS_3, and compute the tree level two and three point functions. These are compared to the large N limit of the W_N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.