# Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization

## TL;DR

This paper uses non-Abelian bosonization dualities to construct and analyze non-Abelian fractional quantum Hall states, including the Read-Rezayi sequence, from Abelian parent states, revealing new dual descriptions and emergent symmetries.

## Contribution

It introduces a novel approach to derive non-Abelian quantum Hall states from Abelian states using 2+1D non-Abelian bosonization dualities, providing new Landau-Ginzburg theories and dual descriptions.

## Key findings

- Constructed Landau-Ginzburg theories for non-Abelian states via pairing mechanisms.
- Derived dual descriptions for generalized Halperin states with emergent symmetries.
- Produced a sequence of non-Abelian states at specific filling fractions through layer clustering.

## Abstract

It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases which can be obtained starting from physically motivated theories of Abelian composite particles. We show that progress on this problem can be made using recently proposed non-Abelian bosonization dualities in 2+1 dimensions, which morally relate $U(N)_k$ and $SU(k)_{-N}$ Chern-Simons-matter theories. The advantage of these dualities is that regions of the phase diagram which may be obscure on one side of the duality can be accessed by condensing local operators on the other side. Starting from parent Abelian states, we use this approach to construct Landau-Ginzburg theories of non-Abelian states through a pairing mechanism. In particular, we obtain the bosonic Read-Rezayi sequence at fillings $\nu=k/(kM+2)$ by starting from $k$ layers of bosons at $\nu=1/2$ with $M$ Abelian fluxes attached. The Read-Rezayi states arise when $k$-clusters of the dual non-Abelian bosons condense. We extend this construction by showing that $N_f$-component generalizations of the Halperin $(2,2,1)$ bosonic states have dual descriptions in terms of $SU(N_f+1)_1$ Chern-Simons-matter theories, revealing an emergent global symmetry in the process. Clustering $k$ layers of these theories yields a non-Abelian $SU(N_f)$-singlet state at filling $\nu = kN_f / (N_f + 1 + kMN_f)$.