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This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions, orbifold theories, and in particular Calabi-Yau compactifications in the late 1980s and early 1990s. At the time these constructions provided a large collection of different vacua, with thousands of explicitly constructed Calabi-Yau manifolds, and estimates of vast numbers of bosonic models, each one associated with its own moduli space. It was clear even then that it would be impossible to systematically search this string vacua landscape. This, however, is not a fundamental problem. Adopting the point of view that any physical theory has to describe not only our universe, but all possible consistent universes, leads to the obvious strategy of using some phenomenological input to select viable models among the ocean of models that obviously do not describe physics as we know it.

In this research thesis, we have analyzed and deepened several Ramanujan equations applied to some sectors of String Theory, Supersymmetry Breaking and Particle Physics. We describe also new possible mathematical connections

The present article is based on a previous one, where a second quantized field theory on the world sheet for summing the planar graphs of phi^3 theory was developed. In this earlier work, the ground state of the model was determined using a variational approximation. Here, starting with the same world sheet theory, we instead use the mean field method to compute the ground state, and find results in agreement with the variational calculation. Apart from serving as a check on the variational calculation, the mean field method enables us to go beyond the ground state to compute the excited states of the model. The spectrum of these states is that of a string with linear trajectories, plus a continuum that starts at higher energy. We show that, by appropriately tuning the parameters of the model, the string spectrum can be cleanly seperated from the continuum.