Dynamical supersymmetry breaking and noncommutative quantum field theory

Abstract

The presence of divergences is certainly one of the main characteristics of the quantum field theory. A way to treat these divergences is through the use of renormalization methods, another one is to look for finite quantum field theories. The hope to find such theories is strong related with Supersymmetry, that improves the ultraviolet behavior of the theories due to a cancellation between bosonic and fermionic divergent contributions. In the 40's decade of the last century, Heisenberg suggested that an uncertainty principle for the coordinates of the spacetime would improve the problem of the ultraviolet divergences that appeared in the perturbative approach in quantum field theory. Currently is given credit that noncommutative theories can be a simple mathematical formulation to represent the proposal of "spacetime foam", i.e., of the idea that in distances of the order of the Planck length, the spacetime loses its continuous structure, and must involve quantum fluctuations of geometry and topology. There are several ways to implement the noncommutativity in quantum field theory, but apparently, all formulations share one same property, the "IR/UV mixing" (infrared/ultraviolet mixing), that is a transmutation of originally UV divergences of the usual theory, to IR divergences in its noncommutative extension. A way to prevent this problem is to work with less UV divergent models. Therefore, natural candidates are supersymmetric theories. However, to construct realistic models of particle physics, Supersymmetry must be broken, because until the moment the supersymmetric partners of the usual particles had not been observed. Therefore it is essential to understand under which conditions supersymmetry can be broken. Thus, our main objective in this project is to study the mechanisms of gauge symmetry and supersymmetry breaking in supersymmetric noncommutative field theories. (AU)