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We solve the Killing spinor equations of 6-dimensional (1,0) superconformaltheories in all cases. In particular, we derive the conditions on the fieldsimposed by the Killing spinor equations and demonstrate that these depend onthe isotropy group of the Killing spinors. We focus on the models proposed bySamtleben et al in \cite{ssw} and find that there are solutions preserving 1,2,4 and 8 supersymmetries. We also explore the solutions which preserve 4supersymmetries and find that many models admit string and 3-brane solitons asexpected from the M-brane intersection rules. The string solitons are smoothregulated by the moduli of instanton configurations.

(1,0) superconformal theories in six dimensions and Killing spinor equations