Title: An Abelian Higgs model for disclinations in nematics
Author(s):

	A. de Pédua Santos (Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil),
	F. Moraes (Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil),
	F. A. N. Santos (Dutch Institute for Emergent Phenomena (DIEP), Institute for Advanced Studies, University of Amsterdam, Oude Turfmarkt 147, 1012 GC, Amsterdam, Netherlands; Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, Netherlands),
	S. Fumeron (Laboratoire de Physique et Chimie Théoriques, UMR Université de Lorraine - CNRS 7019, 54000 Nancy, France)

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.

Key words: analog gravity, liquid crystals, topological defects

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