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We consider the non-abelian theory (http://arxiv.org/abs/arXiv:1203.4224) foran arbitrary number $N_5$ of five-branes and construct self-dual stringsolution with an arbitrary $N_2$ unit of self-dual charges. This generalizesthe previous solution of non-abelian self-dual string(http://arxiv.org/abs/arXiv:1207.1095) of $N_5=2, N_2=1$. The radius-transversedistance relation describing the M2-branes spike, particularly its dependenceon $N_2$ and $N_5$, is obtained and is found to agree precisely with thesupergravity description of an intersecting M2-M5 branes system.

Non-abelian Self-Dual String and M2-M5 Branes Intersection in Supergravity