Rich Structures of Simple Supersymmetric Yang-Mills Theory

The aim of the thesis is to deepen the knowledge of general fundamental properties of classical and quantum field theories via the study of main features of the simplest supersymmetric gauge theory in four-dimensional spacetime, N = 1 super Yang-Mills (SYM) theory. Starting with the study of symmetry properties of this theory, one proceeds to comprehend quantum anomalies affecting some of the symmetries and spontaneous breaking thereof, the phenomenon which leads to a rich structure of the SYM vacua. Then, one will study how different vacua are connected to each other via domain walls, which are examples of topologically-nontrivial solitonic objects appearing in many theoretical models. Finally, a generalization of the Veneziano-Yankielowicz lagrangian is discussed.