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Local gravitational solutions dual to M2-branes intersecting and/or ending on M5-branes

We construct local solutions to eleven-dimensional supergravity describing M2-branes intersecting and/or ending on M5-branes, in the near-horizon limit of the M2-branes. Global solutions describing these theories should have 16 supercharges and asymptotic AdS_4 x S^7 regions, as well as M5-branes wrapping AdS_3 x S^3 subspaces. We construct the local solution describing a stack of an arbitrary number of M5-branes with AdS_3 x S^3 worldvolume and arbitrary M2-brane charge. Our construction provides a mechanism to get around the no-go theorem that rules out the existence of global solutions preserving 16 supercharges interpolating between AdS_7 x S^4 and AdS_4 x S^7 regions.