 Solution

An isolated nematic half-defect reverses the representative director after one circuit. Alignment would then reverse the polar vector, which is not the same physical state. Half-integer defects can therefore occur only if accompanied by a branch wall on which polar order rotates sharply or vanishes. The wall has a tension proportional to its length, so half-defects are confined in pairs in the uniformly polar phase; they can deconfine where polar order disappears.