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

TL;DR

This paper explores the emergence of higher-spin symmetry in 2D $ abla(0,2)$ disordered models, extending previous work by including $E$-type potentials and demonstrating duality and symmetry emergence in the IR regime.

Contribution

It introduces a duality between $E$-type and $J$-type models in $ abla(0,2)$ theories and shows that $E$-type models also exhibit higher-spin symmetry in certain limits.

Findings

$E$-type models are IR equivalent to $J$-type models.

Higher-spin symmetry emerges in $E$-type models under specific conditions.

The results expand the moduli space of $ abla(0,2)$ disordered theories.

Abstract

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.