OM Theory and V-duality

We show that the (M5, M2, M 2′, MW) bound state solution of eleven-dimensional supergravity recently constructed in hep-th/0009147 is related to the (M5, M2) bound state one by a finite Lorentz boost along a M5-brane direction perpendicular to the M2-brane. Given the (M5, M2) bound state as a defining system for OM theory and the above relation between this system and the (M5, M2, M 2′, MW) bound state, we test the recently proposed V-duality conjecture in OM theory. Insisting to have a decoupled OM theory, we find that the allowed Lorentz boost has to be infinitesimally small, therefore resulting in a family of OM theories related by Galilean boosts. We argue that such related OM theories are equivalent to each other. In other words, V-duality holds for OM theory as well. Upon compactification on either an electric or a ``magnetic'' circle (plus T-dualities as well), the V-duality for OM theory gives the known one for either non-commutative open string theories or non-commutative Yang-Mills theories. This further implies that V-duality holds in general for the little m-theory without gravity