  Topological defects in elastic media may be described by a geometric field
akin to three-dimensional gravity. From this point of view, disclinations are
line defects of zero width corresponding to a singularity of the curvature in
an otherwise flat background. On the other hand, in two dimensions, the Frank
free energy of a nematic liquid crystal may be interpreted as an Abelian Higgs
Lagrangian. In this work, we construct an Abelian Higgs model coupled to
"gravity" for the nematic phase, with the perspective of finding more realistic
disclinations. That is, a cylindrically symmetric line defect of finite radius,
invariant under translations along its axis. Numerical analysis of the
equations of motion indeed yield a $+1$ winding number "thick" disclination.
The defect is described jointly by the gauge and the Higgs fields, that compose
the director field, and the background geometry. Away from the defect, the
geometry is conical, associated to a dihedral deficit angle. The gauge field,
confined to the defect, gives a structure to the disclination while the Higgs
field, outside, represents the nematic order.
