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

We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the isotropy group of the Killing spinors. We focus on the models proposed by Samtleben 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 4 supersymmetries and find that many models admit string and 3-brane solitons as expected from the M-brane intersection rules. The string solitons are smooth regulated by the moduli of instanton configurations.