$E$ and $J$ type $\mathcal{N}=(0,2)$ disordered models and higher-spin symmetry

In this work, we investigate the emergence of higher-spin structure in 2d $\mathcal{N}=(0,2)$ disordered models. While previous studies focused on the $J$-type model where the $E$-term in the Fermi multiplet was discarded. We extend the discussion to $\mathcal{N}=(0,2)$ disordered models with $E$-type potential. In terms of (disordered) $\mathcal{N}=(0,2)$ Landau-Ginzburg theory, we establish a duality between two models. By solving the Schwinger-Dyson equations and the ladder kernel matrix for 4-point functions, we verify that the $E$-type model is dynamically equivalent to the $J$-type model in the IR regime. Furthermore, we demonstrate that the $E$-type model also exhibits emergent higher-spin symmetry in certain limits. Our results reveal a larger region of the moduli space of 2D $\mathcal{N}=(0,2)$ disordered theories and provides insights into the holographic transition from finite to tensionless strings that can be diagnosed by the emergence of higher-spin symmetries.