Fluxes and Warping for Gauge Couplings in F-theory

We compute flux-dependent corrections in the four-dimensional F-theory effective action using the M-theory dual description. In M-theory the 7-brane fluxes are encoded by four-form flux and modify the background geometry and Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor which also depends on the torus directions of the compactification fourfold. This dependence is crucial in the derivation of the four-dimensional action, although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are described by an infinite array of Taub-NUT spaces. We use the explicit metric on this geometry to derive the locally corrected warp factor and M-theory three-from as closed expressions. We focus on contributions to the 7-brane gauge coupling function from this M-theory back-reaction and show that terms quadratic in the internal seven-brane flux are induced. The real part of the gauge coupling function is modified by the M-theory warp factor while the imaginary part is corrected due to a modified M-theory three-form potential. The obtained contributions match the known weak string coupling result, but also yield additional terms suppressed at weak coupling. This shows that the completion of the M-theory reduction opens the way to compute various corrections in a genuine F-theory setting away from the weak string coupling limit.Comment: 46 page

Holomorphic variables in magnetized brane models with continuous Wilson lines

We analyze the action of the target-space modular group in toroidal type IIB orientifold compactifications with magnetized D-branes and continuous Wilson lines. The transformation of matter fields agree with that of twisted fields in heterotic compactifications, constituting a check of type I/heterotic duality. We identify the holomorphic N = 1 variables for these compactifications. Matter fields and closed string moduli are both redefined by open string moduli. The redefinition of matter fields can be read directly from the perturbative Yukawa couplings, whereas closed string moduli redefinitions are obtained from D-brane instanton superpotential couplings. The resulting expressions reproduce and generalize, in the presence of internal magnetic fields, previous results in the literature.Comment: 9 pages, no figures; v2: conventions for Wilson lines changed, major simplifications in expressions, discussions extended, typos corrected, some references adde

Moduli Redefinitions and Moduli Stabilisation

Field redefinitions occur in string compactifications at the one loop level. We review arguments for why such redefinitions occur and study their effect on moduli stabilisation and supersymmetry breaking in the LARGE volume scenario. For small moduli, although the effect of such redefinitions can be larger than that of the $\alpha'$ corrections in both the K\"ahler and scalar potentials, they do not alter the structure of the scalar potential. For the less well motivated case of large moduli, the redefinitions can dominate all other terms in the scalar potential. We also study the effect of redefinitions on the structure of supersymmetry breaking and soft terms.Comment: 21 pages, 3 figures; v2. references adde

Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on T6/Z6'

The perturbative leading order open string three-point couplings for the Standard Model with hidden USp(6) on fractional D6-branes on T6/Z6' from arXiv:0806.3039 [hep-th], arXiv:0910.0843 [hep-th] are computed. Physical Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times a non-holomorphic prefactor involving the corresponding classical open string Kaehler metrics are given, and mass terms for all non-chiral matter states are derived. The lepton Yukawa interactions are at leading order flavour diagonal, while the quark sector displays a more intricate pattern of mixings. While N=2 supersymmetric sectors acquire masses via only two D6-brane displacements - which also provide the hierarchies between up- and down-type Yukawas within one quark or lepton generation -, the remaining vector-like states receive masses via perturbative three-point couplings to some Standard Model singlet fields with vevs along flat directions. Couplings to the hidden sector and messengers for supersymmetry breaking are briefly discussed.Comment: 52 pages (including 8p. appendix); 5 figures; 14 tables; v2: discussion in section 4.1.3 extended, footnote 5 added, typos corrected, accepted by JHE

Non-perturbative Vacuum Destabilization and D-brane Dynamics

We analyze the process of string vacuum destabilization due to instanton induced superpotential couplings which depend linearly on charged fields. These non-perturbative instabilities result in potentials for the D-brane moduli and lead to processes of D-brane recombination, motion and partial moduli stabilization at the non-perturbative vacuum. By using techniques of D-brane instanton calculus, we explicitly compute this scalar potential in toroidal orbifold compactifications with magnetized D-branes by summing over the possible discrete instanton configurations. We illustrate explicitly the resulting dynamics in globally consistent models. These instabilities can have phenomenological applications to breaking hidden sector gauge groups, open string moduli stabilization and supersymmetry breaking. Our results suggest that breaking supersymmetry by Polonyi-like models in string theory is more difficult than expected.Comment: 61 pages, 6 figures, 5 tables; Minor corrections, version published in JHE