Extended higher spin holography and Grassmannian models

TL;DR

The paper proposes holographic dualities between higher spin gravity theories on AdS$_3$ extended with a U($M$) Chan-Paton factor and large-$N$ Grassmannian coset CFTs, both in bosonic and ${ m N}=2$ supersymmetric settings. It develops the bulk theories (including a bosonic truncation and the full ${ m N}=2$ supergravity) and derives their one-loop partition functions, then identifies dual CFTs as Grassmannian cosets whose 't Hooft limits reproduce the bulk spectra and symmetries. The free limits of these CFTs exhibit the expected higher spin symmetries, and explicit CFT constructions of currents in the 't Hooft limit are matched to bulk currents, supporting the bulk-boundary correspondence. The work demonstrates that Grassmannian models interpolate between vector-like theories dual to higher spin gravity and matrix-like theories related to ABJ-type string theories, suggesting a unified framework linking higher spin holography and string theory in lower dimensions.

Abstract

We propose holographic dualities between higher spin gravity theories extended with Chan-Paton factor on AdS_3 and a large N limit of two dimensional Grassmannian models with and without supersymmetry. These proposals are natural extensions of the duality without Chan-Paton factor, and the extensions are motivated by a higher dimensional version of the duality, which implies a possible relation to superstring theory via ABJ theory. As evidence for the proposals, we show that the free limit of the Grassmannian models have the higher spin symmetry expected from the dual gravity theory. Furthermore, we construct currents in the 't Hooft limit of the supersymmetric Grassmannian model and compare them with the currents from the bulk theory. One-loop partition function of the supergravity theory is reproduced by the 't Hooft limit of the Grassmannian model after decoupling a gauge sector.