The non-linear nature of string theory on non-trivial backgrounds related to the AdS/CFT correspondence suggests to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit which de
scribes point-like strings and the so called near flat space limit which connects two different sectors of string theory -- pp-waves and giant magnons. Recently another example of AdS/CFT duality emerged - $AdS_4/CFT_3$, which suggests duality between $mathcal N=6$ CS theory and superstring theory on $AdS_4times cp$. In this paper we study the near flat space limit of strings on the $AdS_4times cp$ background and discuss possible applications of the reduced theory.
Recently Maldacena and Swanson suggested a new limit of string theory on the $AdS_5times S^5$ background, the so called near flat space limit. The resulting reduced theory interpolates between the pp-wave limit and giant magnon type string solutions.
It was shown that the reduced model possess many features of the original theory. On the other hand, theories with less supersymmetry are of great importance for the string/gauge theory correspondence. In this paper we study the near flat limit reduction of string theory on the Maldacena-Nunez background, which is dual to $N=1$ Yang-Mills theory. The reduced model interpolates between the pp-wave limit and a certain magnon type subsector of the theory. The similarity of the structures of the reduced model obtained here and that by Maldacena and Swanson indicates the possibility of existence of integrable subsectors of strings on the Maldacena-Nunez background.
