Non-abelian descendant of abelian duality in a two-dimensional frustrated quantum magnet

TL;DR

This paper presents a novel duality between an O(4) vector model and a fermionic gauge theory in two dimensions, providing non-perturbative insights into quantum criticality in frustrated magnetic systems.

Contribution

It introduces a new duality involving non-abelian symmetry and fermions in 2D, derived from a frustrated XY model, expanding understanding of quantum critical points beyond traditional theories.

Findings

Duality between O(4) vector model and Dirac fermion gauge theory.

Emergence of non-abelian symmetry at low energies.

Connection to abelian boson-vortex duality in lattice models.

Abstract

Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson paradigm have led to a number of field theories, potentially important for certain two-dimensional magnetic insulating systems, where criticality is not very well understood. This situation highlights the need for non-perturbative information about criticality in two spatial dimensions (three space-time dimensions), which is a longstanding challenge. As a step toward addressing these issues, we present evidence that the O(4) vector model is dual to a theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both field theories arise as low-energy, long-wavelength descriptions of a frustrated XY model on the triangular lattice. Abelian boson-vortex duality of the lattice model, together with the emergence of larger non-abelian symmetry at low energies, leads to this rare example of duality in two spatial dimensions involving non-abelian global symmetry and fermions, but without supersymmetry. The duality can also be viewed as a bosonization of the Dirac fermion gauge theory.