Equivalence between vortices, twists, and chiral gauge fields in the Kitaev honeycomb lattice model

We demonstrate that Z₂ gauge transformations and lattice deformations in Kitaev's honeycomb lattice model can have the same description in the continuum limit in terms of a chiral gauge field. The chiral gauge field is coupled to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the Z₂ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding π vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realize in experiments.