Abstract
We argue that the moduli space for the Bagger-Lambert
A4 theory at level k is (
8 × 8)/D2k, where D2k is the dihedral group of order
4k. We conjecture that the theory describes two M2-branes on a
2k ``M-fold'', in which a geometrical action of 2k is
combined with an action on the branes. For k = 1, this arises as the
strong coupling limit of two D2-branes on an O2− orientifold, whose
worldvolume theory is the maximally supersymmetric SO(4) gauge
theory. Finally, in an appropriate large-k limit we show that one
recovers compactified M-theory and the M2-branes reduce to D2-branes.