We have measured the thermal conductivity along the [101] direction, kappa_[101]_, along the [10-1] direction, kappa_[10-1]_, and along the b-axis, kappa_b_, of the quasi one-dimensional S=1/2 spin system Sr_2_V_3_O_9_ in magnetic fields up to 14 T, in order to find the thermal conductivity due to spinons and to clarify whether the spin-chains run along the [101] or [10-1] direction. It has been found that both kappa_[101]_, kappa_[10-1]_ and kappa_b_ show one peak around 10 K in zero field and that the magnitude of kappa_[10-1]_ is larger than those of kappa_[101]_ and kappa_b_. By the application of magnetic field along the heat current, the peak of kappa_[10-1]_ is markedly suppressed, while the peaks of kappa_[101]_ and kappa_b_ little change. These results indicate that there is a large contribution of spinons to kappa_[10-1]_ and suggest that the spin-chains run along the [10-1] direction.
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