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We present a nonabelian Lagrangian that appears to have $(2,0)$superconformal symmetry and that can be coupled to a supergravity background.But for our construction to work, we have to break this superconformal symmetryby imposing as a constraint on top of the Lagrangian that the fields havevanishing Lie derivatives along a Killing direction.

A nonabelian M5 brane Lagrangian in a supergravity background