On type IIA Penrose limit and N = 6 Chern-Simons theories

Recently, Aharony, Bergman, Jafferis and Maldacena proposed that the N = 6 Chern-Simons gauge theories are holographically dual to the M-theory backgrounds with multiple M2-branes on orbifolds C4/Zk. When k is large, they have the type IIA string description. In this paper we analyze the Penrose limit of this IIA background and express the string spectrum as the conformal dimensions of operators in the gauge theories. For BPS operators, we can confirm the agreements between the IIA string on plane waves and the gauge theories. We point out that there exist BMN-like operators in the gauge theories, though their holographic interpretation does not seem to be simple. Also we analyze the weak coupling limit of this theory and show that the Hagedorn/deconfinement transition occurs as expected.