Higher-Spin Poisson Sigma Models and Holographic Duality for SYK Models

Abstract

SYK models provide an interesting playground for exploring the $Ad{S}_2/CF{T}_1$ correspondence. We focus on a class of SYK models that exhibit higher-spin symmetry, whose gravity sector is described by a BF theory generalizing Jackiw--Teitelboim gravity to higher spins. We further develop this framework by constructing consistent interactions between higher-spin gauge fields and scalar matter fields. Two concrete realizations are proposed: Model A, arising from a deformation of the universal enveloping algebra of $\mathfrak{sl}(2,\mathbb{R})$, and Model B, a perturbatively local Poisson sigma-model with an infinite-dimensional target space. While both capture higher-spin dynamics on $(A)d{S}_2$, they differ in their algebraic structures and locality properties, thus offering complementary perspectives on higher-spin holography.

30 pages + Appendices = 42 pages