Construction of Supersymmetric Field Theories

Though supersymmetry remains a topic of contention, it provides a fruitful avenue of exploration into new physical theories and mathematical ideas. Supersymmetry gives a natural extension of the Standard Model of particle physics, providing a new symmetry to connect half-integer and integer spin particles (fermions and bosons, respectively). Fermions, which constitute particles of matter, and bosons, force-carrying particles, are upgraded to the same standing and thus gain the same equations of motion under supersymmetry.

We introduce the mechanics of incorporating supersymmetry into toy models and present several potential solutions to problems plaguing the standard model today. Then, a brief overview is given on how to incorporate gravity into a supersymmetric standard model, with everything coalescing in Supergravity.