Abstract
It is shown that vortices in linearly polarized polariton condensates in planar semiconductor microcavities carry two winding numbers (k, m). These numbers can be either integer or half-integer simultaneously. Four half-integer vortices (1/2, 1/2), (-1/2, -1/2), (1/2, -1/2), and (-1/2, 1/2) are anisotropic, possess the smallest energy, and define the Kosterlitz-Thouless transition temperature. The condensate concentration remains finite within the core of the half vortex and the condensate polarization becomes fully circular in the core center.
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