Fluctuations of topological disclination lines in nematics: renormalization of the string model

The fluctuation eigenmode problem of the nematic topological disclination line with strength $\pm 1/2$ is solved for the complete nematic tensor order parameter. The line tension concept of a defect line is assessed, the line tension is properly defined. Exact relaxation rates and thermal amplitudes of the fluctuations are determined. It is shown that within the simple string model of the defect line the amplitude of its thermal fluctuations is significantly underestimated due to the neglect of higher radial modes. The extent of universality of the results concerning other systems possessing line defects is discussed.