Higher Derivative Terms in Three Dimensional Supersymmetric Theories

In this work, we systematically analyze higher derivative terms in the supersymmetric effective actions for three dimensional scalar field theories using $\mathcal{N} =1$ superspace formalism. In these effective actions, we show that auxiliary fields do not propagate and their effective actions can be expressed in terms of the physical fields. So, the theory does not change its field content upon addition of higher derivative terms. We use derivative expansion to generate four, five and six dimensional terms for an interacting scalar field theory with $\mathcal{N} =1$ supersymmetry. We show that along with pure fermionic and bosonic terms, there are various five and six dimensional topological terms that mix bosonic and fermionic fields. Finally, we use these results to obtain higher derivative topological terms in the effective action for two M2-branes.