One loop phenomenology of type II string theory : intersecting d-branes and noncommutativity
We examine one loop amplitudes for open and closed strings in certain D-brane configurations, and investigate the consequences for phenomenology. Initially we consider open strings at D6-brane intersections. We develop techniques for one-loop diagrams. The one-loop propagator of chiral intersection states is calculated exactly and its finiteness is shown to be guaranteed by RR tadpole cancellation. The result is used to demonstrate the expected softening of power law running of Yukawa couplings at the string scale. We also develop methods to calculate arbitrary TV-point functions at one-loop, including those without gauge bosons in the loop. These techniques are also applicable to heterotic orbifold models. One issue of the intersecting D6-brane models is that the Yukawa couplings of the simpler models suffer from the so-called "rank one" problem - there is only a single non-zero mass and no mixing. We consider the one-loop contribution of E2-instantons to Yukawa couplings on intersecting D6-branes, and show that they can provide a solution. In addition they have the potential to provide a geometric explanation for the hierarchies observed in the Yukawa couplings. In order to do this we provide the necessary quantities for instanton calculus in this class of background. We then explore how the IR pathologies of noncommutative field theory are resolved when the theory is realized as open strings in background B-fields: essentially, since the IR singularities are induced by UV/IR mixing, string theory brings them under control in much the same way as it does the uv singularities. We show that at intermediate scales (where the Selberg-Witten limit is a good approximation) the theory reproduces the noncommutative field theory with all the (un)usual features such as UV/IR mixing, but that outside this regime, in the deep infra-red, the theory flows continuously to the commutative theory and normal Wilsoman behaviour is restored. The resulting low energy physics resembles normal commutative physics, but with additional suppressed Lorentz violating operators. We also show that the phenomenon of UV/IR mixing occurs for the graviton as well, with the result that, in configurations where Planck's constant receives a significant one-loop correction (for example brane-induced gravity), the distance scale below which gravity becomes non-Newtonian can be much greater than any compact dimensions.