Title:

Duality and models of supersymmetry breaking

Duality is often most clearly manifest in supersymmetric theories, where the rigid mathematical structure affords good control over the behaviour of the system. In many realworld applications, and particularly in particle physics at the TeV scale, supersymmetry can only be present as a broken symmetry. In this thesis we explore various situations in which duality can continue be important when supersymmetry is broken spontaneously, or even explicitly. We first focus on the AdS/CFT correspondence, and consider the effect of instantons in a nonsupersymmetric gauge theory obtained via a marginal deformation of N = 4 super YangMills. This gauge theory is expected to be dual to type IIB string theory on a background that is the product of fivedimensional antide Sitter spacetime and a deformed fivesphere. By performing an instanton calculation in the deformed gauge theory we extract a prediction for the dilatonaxion field in dual string theory. In the limit of small deformations where the supergravity regime is valid, our instanton result reproduces the expression for the axiodilaton of the supergravity solution originally found by Frolov, thus supporting the validity of the correspondence. We then go on to look at how supersymmetry breaking in a metastable vacuum allows one to build simple and concrete models of gauge mediation. In the prototypical model of Intriligator, Seiberg and Shih (ISS), Seiberg duality plays an important role in ensuring the longevity of the metastable vacuum. In a move to construct more realistic models we deform the ISS model by adding a baryon term to the superpotential. This simple deformation causes spontaneous breaking of the approximate Rsymmetry of the metastable vacuum. We then gauge an SU(5) flavour group and identify it with the parent gauge symmetry of the supersymmetric Standard Model. This implements direct mediation of supersymmetry breaking without the need for an additional messenger sector. A reasonable choice of parameters leads to gaugino masses of the right order. To further explore the phenomenology of metastable susy breaking we distinguish different types of models by the manner in which Rsymmetry is broken in the metastable vacuum. In general, there are two possible ways to break Rsymmetry: explicitly or spontaneously. We find that the MSSM phenomenology can be greatly affected how this breaking occurs in the Hidden Sector. Explicit Rsymmetry breaking models lead to fairly standard gauge mediation patterns, but we argue that in the context of ISStype models this only makes sense if B = 0 at the mediation scale. This leads to high values of tan beta as a generic prediction. If on the other hand Rsymmetry is broken spontaneously, then Rviolating soft terms tend to be suppressed with respect to the Rsymmetry preserving ones, and one is led to a scenario with large scalar masses. These models interpolate between standard gauge mediation and split SUSY models. We provide benchmark points for the two scenarios, which serve to demonstrate that the specific dynamics of the Hidden Sector  the underlying nature of supersymmetry and Rsymmetry breaking  can considerably affect the mass spectrum of the MSSM.
