Fermionic dualities with axial gauge fields

TL;DR

This paper develops new dualities involving axial gauge fields in 2+1 and 3+1 dimensions, providing insights into topological semimetals and breaking Lorentz invariance, with potential implications for experimental observations.

Contribution

It introduces axial field theory dualities using an axial slave-rotor approach, extending dualities to systems with axial gauge fields and Lorentz symmetry breaking.

Findings

Duality suggests a critical surface theory for strained topological insulators.

Maps free Dirac fermions to those coupled with emergent gauge fields.

Indicates robustness of quantized effects in interacting Weyl semimetals.

Abstract

The dualities that map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. However, simplifying assumptions such as Lorentz invariance, low dimensionality, or the absence of axial gauge fields, limit their application to a broad class of systems, including topological semimetals. Here we derive several axial field theory dualities in 2+1 and 3+1 dimensions by developing an axial slave-rotor approach capable of accounting for the axial anomaly. Our 2+1-dimensional duality suggests the existence of a dual, critical surface theory for strained three-dimensional non-symmorphic topological insulators. Our 3+1-dimensional duality maps free Dirac fermions to Dirac fermions coupled to emergent U(1) and Kalb-Ramond vector and axial gauge fields. Upon fixing an axial field configuration that breaks Lorentz invariance, this duality maps free to interacting Weyl semimetals, thereby suggesting that the quantization of the non-linear circular photogalvanic effect can be robust to certain interactions. Our work emphasizes how axial and Lorentz-breaking dualities improve our understanding of topological matter.