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We show that line defects in a non-Abelian Kitaev spin liquid harbor gaplessone-dimensional Majorana modes if the interaction across the defect falls belowa critical value. Treating the weak interaction at the line defect within amean-field approximation, we determine the critical interaction strength as afunction of the external magnetic field. In the gapless regime, we use thelow-energy effective field theory to calculate the spin-lattice relaxation ratefor a nuclear spin near the defect and find a cubic temperature dependence thatagrees with experiments in the Kitaev material $\alpha\text{-RuCl}_3$.

Gapless excitations in non-Abelian Kitaev spin liquids with line defects