Lorentz Transformation and Light-Like Noncommutative SYM

We show that combining the spatial noncommutative SYM limit and Lorentz transformation, one can obtain a well-behaved light-like noncommutative SYM limit. 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 transformation. Along this line, we obtain the supergravity dual for the light-like noncommutative SYM, which is the same as the one acquired using a different method. As a comparison, the supergravity duals for the ordinary SYM, spatial noncommutative SYM and the noncommutative open string theories are given as well, in an infinitely-boosted frame with finite momentum density, which are the decoupling limits of bound states (Dp, W), (D($p-2$), W, Dp), and (F1, W, Dp), respectively.