Lorentz transformation and light-like noncommutative SYM

We show that combining the spatial noncommutative SYM limit and Lorentz tra nsformation, one can obtain a well-behaved light-like noncommutative SYM li mit. The light-like noncommutative SYM is unitary. When the boost velocity is finite, the resulting theory with space-time noncommutativity is unitary as well. The light-like noncommutative SYM limit can also be approached by combining the noncommutative open string theory limit and Lorentz transfor mation. Along this line, we obtain the supergravity dual for the light-like noncommutative SYM, which is the same as the one acquired using a differen t method. As a comparison, the supergravity duals for the ordinary SYM, spa tial noncommutative SYM and the noncommutative open string theories are giv en as well, in an infinitely-boosted frame with finite momentum density, wh ich are the decoupling limits of bound states (Dp, W), (D(p - 2), W, Dp), a nd (F1, W, Dp), respectively.