Disclination asymmetry in two-dimensional nematic liquid crystals with unequal Frank constants

The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for +{} and -{} disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.