Higher spin AdS_3 supergravity and its dual CFT

TL;DR

The paper extends higher-spin AdS$_3$ holography to a supersymmetric setting by proposing a duality between Vasiliev’s higher-spin supergravity with symmetry $\text{shs}[\lambda]$ and the $\mathcal{N}=(2,2)$ $\mathbb{C}P^N$ Kazama–Suzuki coset in the large $N$ ’t Hooft limit with fixed $\lambda$. The authors construct the bulk theory as a Chern–Simons system based on $\text{sl}(N+1|N)$ (or its higher-spin limit) and compute the one-loop partition function, including a new treatment of higher-spin fermions, and match it to the dual CFT vacuum character and selected massive-matter contributions. They show that the bulk partition function factorizes into supersymmetric pieces consistent with the coset spectrum, and they uncover a strong-weak self-duality under $\lambda\rightarrow 1-\lambda$, interpreted as a level-rank duality on the CFT side. The work provides several nontrivial consistencies between the bulk and boundary theories and outlines future tests (e.g., elliptic genus, RG analysis, $1/N$ corrections) to solidify the duality. The results deepen the understanding of holography for interacting higher-spin theories and SUSY coset CFTs and suggest robust tools for probing quantum gravity in a controlled setting.

Abstract

Vasiliev's higher spin supergravity theory on three dimensional anti-de Sitter space is studied and, in particular, the partition function is computed at one loop level. The dual conformal field theory is proposed to be the N=(2,2) CP^N Kazama-Suzuki model in two dimensions. The proposal is based on symmetry considerations and comparison of the bulk partition function with the conformal field theory. Our findings suggest that the theory is strong-weak self-dual.