SUPERSPACE COMPUTATIONS IN SUSY AND SUGRA THEORIES

In this thesis, we present two current topics in theoretical high energy physics: We construct the Lagrangian of a deformed supergravity theory on a manifold with a non-trivial spacetime boundary by using the geometric (or rheonomic) approach and we discuss and analyze the supersymmetry invariance of the theory. Separately, we compute some scattering amplitudes in a supersymmetric conformal field theory with the Superspace formalism and Feynman superdiagrams. These two different topics conceptually achieve a contact point through the so-called AdS/CFT duality, which is actually one of the most flourishing fields in theoretical physics today. In the supergravity limit of string theory, this duality outlines a one-to-one correspondence between operators in the CFT on the boundary and the fields of the supergravity theory in the bulk. It could constitute a possible theoretical path towards the building of a theory of quantum gravity, which is the last piece needed to complete the puzzle of unified fundamental interactions. Precisely, we first give an overview of some aspects about supersymmetry, supergravity and AdS/CFT duality, in order to introduce the main two parts of the thesis: On one hand, the study of a particular supergravity theory, which will be referred to as D = 4 generalized AdS-Lorentz deformed supergravity theory, in the presence of a non-trivial boundary (that is when the boundary of spacetime is not thought as set at infinity); on the other hand, the computation of a 1-loop MHV reduced amplitude in N = 2 SCQCD (in D = 4). In the first topic discussed in this thesis, supersymmetry is understood as a local symmetry; indeed, we are dealing with a supergravity theory. On the converse, in the second part of this dissertation, supersymmetry is a global symmetry.