Constructing Operator Bases in N=1 Supersymmetry

We develop two different approaches to construct the operator basis in N=1 supersymmetry. The operators are written in terms of superfields rather than component fields and we make use of the superspace formalism. We focus on higher dimensional operators and non-factorizable interactions and work with the effective field theory framework. We introduce a Hilbert series approach to build the operator basis with both chiral and vector superfields. We propose the notion of "correction space" and give explicitly the form of the corrections that remove redundancies due to the equations of motion and integration by parts. In addition, we derive the maps between the correction spaces. The method proposed here can be applied to both abelian and non-abelian gauge theories with any set of matter fields. We develop a Young diagram approach to constructing higher dimensional operators formed from massless superfields and their superderivatives in N=1 supersymmetry. These operators are in one-to-one correspondence with non-factorizable terms in on-shell superamplitudes, which can be studied with massless spinor-helicity techniques. By relating all spinor-helicity variables to certain representations under a hidden $U(N)$ symmetry behind the theory, we show each non-factorizable superamplitude can be identified with a specific Young tableau. The desired tableau is picked out of a more general set of $U(N)$ tensor products by enforcing the supersymmetric Ward identities. We then relate these Young tableaux to higher dimensional superfield operators and list the rules to read operators directly from the Young tableau. We further explore the diagrammatic approach and develop a semi-standard Young tableau approach to construct an explicit basis. This amplitude basis can be directly translated to a basis for higher dimensional supersymmetric operators, yielding both the number of independent operators and their form. We deal with distinguishable (massless) chiral/vector superfields at first, then generalize the result to the indistinguishable case.