We calculate the scalar gravitational and matter perturbations in the context of slow-roll inflation with multiple scalar fields, that take values on a (curved) manifold, to first order in slow roll. For that purpose a basis for these perturbations determined by the background dynamics is introduced and multiple field slow-roll functions are defined. To obtain analytic solutions to first order, the scalar perturbation modes have to be treated in three different regimes. Consistency of the various approximations fixes their matching times. Multiple field effects in the gravitational potential are due to the rotation of the basis and to the particular solution caused by the coupling to the field perturbation perpendicular to the field velocity. They can contribute even to leading order if the corresponding multiple field slow-roll function is sizable during the last 60 e-folds. The analytical results are illustrated and checked numerically with the example of a quadratic potential.

We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric Standard Model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultra-violet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications of dispersion relations at high energies thereby escaping constraints from astrophysical searches for Lorentz violation.

We describe blowups of C n /Z n orbifolds as complex line bundles over CP n−1 . We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n−1) bundle. Both blowups and their gauge bundles are given explicitly. We investigate ten dimensional SO(32) super Yang-Mills theory coupled to supergravity on these backgrounds. The integrated Bianchi identity implies that there are only a finite number of U(1) bundle models. We describe how the orbifold gauge shift vector can be read off from the gauge background. In this way we can assert that in the blow down limit these models correspond to heterotic C 2 /Z 2 and C 3 /Z 3 orbifold models. (Only the Z 3 model with unbroken gauge group SO(32) cannot be reconstructed in blowup without torsion.) This is confirmed by computing the charged chiral spectra on the resolutions. The construction of these blowup models implies that the mismatch between type-I and heterotic models on T 6 /Z 3 does not signal a complication of S-duality, but rather a problem of type-I model building itself: The standard type-I orbifold model building only allows for a single model on this orbifold, while the blowup models give five different models in blow down.

The theory of Supersymmetric Quantum Electrodynamics is extended by interactions with external vector and tensor backgrounds, that are assumed to be generated by some Lorentz-violating (LV) dynamics at an ultraviolet scale perhaps related to the Planck scale.

In the context of a five dimensional N=1 Kaluza Klein model compactified on S 1 /Z 2 × Z 2 we compute the one-loop gauge corrections to the self energy of the (zero-mode) scalar field. The result is quadratically divergent due to the appearance of a Fayet-Iliopoulos term.

Heterotic orbifolds provide promising constructions of MSSM-like models in string theory. We investigate the connection of such orbifold models with smooth Calabi-Yau compactifications by examining resolutions of the T 6 / 6-II orbifold (which are far from unique) with Abelian gauge fluxes. These gauge backgrounds are topologically characterized by weight vectors of twisted states; one per fixed point or fixed line. The VEV's of these states generate the blowup from the orbifold perspective, and they reappear as axions on the blowup. We explain methods to solve the 24 resolution dependent Bianchi identities and present an explicit solution. Despite that a solution may contain the MSSM particle spectrum, the hypercharge turns out to be anomalous: Since all heterotic MSSM orbifolds analyzed so far have fixed points where only SM charged states appear, its gauge group can only be preserved provided that those singularities are not blown up. Going beyond the comparison of purely topological quantities (e.g. anomalous U(1) masses) may be hampered by the fact that in the orbifold limit the supergravity approximation to lowest order in α ′ is breaking down.

We investigate the properties of localized anomalous U(1)'s in heterotic string theory on the orbifold T 6 /Z 3 . We argue that the local four dimensional and original ten dimensional Green-Schwarz mechanisms can be implemented simultaneously, making the theory manifestly gauge invariant everywhere, in the bulk and at the fixed points. We compute the shape of the Fayet-Iliopoulos tadpoles, and cross check this derivation for the four dimensional auxiliary fields by a direct calculation of the tadpoles of the internal gauge fields. Finally we study some resulting consequences for spontaneous symmetry breaking, and derive the profile of the internal gauge field background over the orbifold.

We construct an MSSM with three generations from the heterotic string compactified on a smooth 6D internal manifold using Abelian gauge fluxes only. The compactification space is obtained as a resolution of the T 6 / 2 × 2 × 2,free orbifold. The 2,free involution of such a resolution breaks the SU(5) GUT group down to the SM gauge group using a suitably chosen (freely acting) Wilson line. Surprisingly, the spectrum on a given resolution is larger than the one on the corresponding orbifold taking into account the branching and Higgsing due to the blow-up modes. The existence of extra resolution states is closely related to the fact that the resolution procedure is not unique. Rather, the various resolutions are connected to each other by flop transitions.