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

Liang Wang, Miao Wang

TL;DR

This work studies higher-spin structure in 2d $\mathcal{N}=(0,2)$ disordered models with nonzero $E$-type potentials. It develops a dual $(0,2)$ Landau-Ginzburg description relating $E$-type and $J$-type configurations, and confirms IR equivalence via Schwinger-Dyson equations and the ladder kernel. The analysis shows that the $E$-type model, like the $J$-type, exhibits emergent higher-spin symmetry in the IR, with a coupling-independent kernel determinant supporting a higher-spin spectrum and vanishing chaos in certain limits, suggesting a holographic connection to tensionless strings. By extending the moduli space of 2D disordered theories, the results provide new insights into the boundary dynamics of higher-spin AdS$_3$ holography and potential bulk duals. The work thus broadens the landscape of solvable disordered systems with higher-spin structure and informs holographic transitions in string theory.

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.

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

TL;DR

This work studies higher-spin structure in 2d disordered models with nonzero -type potentials. It develops a dual Landau-Ginzburg description relating -type and -type configurations, and confirms IR equivalence via Schwinger-Dyson equations and the ladder kernel. The analysis shows that the -type model, like the -type, exhibits emergent higher-spin symmetry in the IR, with a coupling-independent kernel determinant supporting a higher-spin spectrum and vanishing chaos in certain limits, suggesting a holographic connection to tensionless strings. By extending the moduli space of 2D disordered theories, the results provide new insights into the boundary dynamics of higher-spin AdS holography and potential bulk duals. The work thus broadens the landscape of solvable disordered systems with higher-spin structure and informs holographic transitions in string theory.

Abstract

In this work, we investigate the emergence of higher-spin structure in 2d disordered models. While previous studies focused on the -type model where the -term in the Fermi multiplet was discarded. We extend the discussion to disordered models with -type potential. In terms of (disordered) 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 -type model is dynamically equivalent to the -type model in the IR regime. Furthermore, we demonstrate that the -type model also exhibits emergent higher-spin symmetry in certain limits. Our results reveal a larger region of the moduli space of 2D 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.
Paper Structure (14 sections, 43 equations, 1 table)

This paper contains 14 sections, 43 equations, 1 table.

Table of Contents

  1. Introduction
  2. Duality of the $(0,2)$ Landau-Ginzburg Model
  3. Setup Superfields
  4. Symmetry in the $(0,2)$ Landau Ginzburg Action
  5. Calculations in the $E$-type Model
  6. Model Settings and Action
  7. $G\Sigma$ Action and SD Equations
  8. Two-Point Functions
  9. Four-Point Functions
  10. $J$ type model and Higher Spin
  11. Ladder Diagram and Kernel
  12. Evidence of Higher Spin Symmetry
  13. Conclusion and Outlook
  14. Appendix