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We study supersymmetric branes in AdS_7 x S^4 and AdS_4 x S^7. We show thatin the former case the membranes should be viewed as M5 branes with fluxes andwe identify two types of such fivebranes (they are analogous to giant gravitonsand to dual giants). In AdS_4 x S^7 we find both M5 branes with fluxes andfreestanding stacks of membranes. We also go beyond probe approximation andconstruct regular supergravity solutions describing geometries produced by thebranes. The metrics are completely specified by one function which satisfieseither Laplace or Toda equation and we give a complete classification ofboundary conditions leading to smooth geometries. The brane configurationsdiscussed in this paper are dual to various defects in three- andsix-dimensional conformal field theories.

1/2-BPS states in M theory and defects in the dual CFTs