Higher spin AdS_3 holography with extended supersymmetry

TL;DR

The paper advances a holographic program for AdS$_3$/CFT$_2$ by linking higher spin gravity with extended supersymmetry to large $N$ Grassmannian/Kazama–Suzuki coset CFTs at critical levels, demonstrating one-loop partition function matching and constructing explicit low-spin symmetry generators. It identifies an ${\cal N}=3$ enhanced supersymmetry in a Grassmannian KS model at $k=N+M$, suggesting a path to a 3d higher-spin–string dual via AdS$_3\times M_7$, and analyzes BPS spectra and marginal deformations relevant to breaking higher spin symmetries. The work further explores a truncation at $\lambda=1/2$ that yields so$(p{+}1)$-extended SUSY algebras from so$(p)$ scaffolds, supported by an orbifold CFT construction that mirrors bulk truncations and yields a complementary dual candidate. Together, these results articulate a network of dualities (including a potential ABJ-like triality in lower dimensions) among higher spin theories, supersymmetric cosets, and string theory, with concrete checks via partition functions and OPE/algebra structures.

Abstract

We propose a holographic duality between a higher spin AdS_3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k=N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an N=3 supersymmetry of critical level model at finite k,N. In particular, we examine BPS states and marginal deformations. Inspired by the supergravity side, we also propose and test another large N CFT dual obtained as a Z_2 automorphism truncation of a similar coset model, but at a non-critical level.