Dirac fermions on a disclinated flexible surface

A self-consisting gauge-theory approach to describe Dirac fermions on flexible surfaces with a disclination is formulated. The elastic surfaces are considered as embeddings into $R^3$ and a disclination is incorporated through a topologically nontrivial gauge field of the local $SO(3)$ group which generates the metric with conical singularity. A smoothing of the conical singularity on flexible surfaces is naturally accounted for by regarding the upper half of two-sheet hyperboloid as an elasticity-induced embedding. The availability of the zero-mode solution to the Dirac equation is analyzed.