Duality and Models of Supersymmetry Breaking

Abstract

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 real-world 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 non-supersymmetric gauge theory obtained via a marginal deformation of N = 4 super Yang-Mills. This gauge theory is expected to be dual to type IIB string theory on a background that is the product of five-dimensional anti-de Sitter spacetime and a deformed five-sphere. By performing an instanton calculation in the deformed gauge theory we extract a prediction for the dilaton-axion 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 axio-dilaton 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 R-symmetry 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 R-symmetry is broken in the metastable vacuum. In general, there are two possible ways to break R-symmetry: explicitly or spontaneously. We find that the MSSM phenomenology can be greatly affected how this breaking occurs in the Hidden Sector. Explicit R-symmetry breaking models lead to fairly standard gauge mediation patterns, but we argue that in the context of ISS-type 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 R-symmetry is broken spontaneously, then R-violating soft terms tend to be suppressed with respect to the R-symmetry 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 R-symmetry breaking - can considerably affect the mass spectrum of the MSSM.