Type IIB Flux Vacua from M-theory via F-theory

We study in detail some aspects of duality between type IIB and M-theory. We focus on the duality between type IIB string theory on K3 x T^2/Z_2 orientifold and M-theory on K3 x K3, in the F-theory limit. We give the explicit map between the fields and in particular between the moduli of compactification, studying their behavior under the F-theory limit. Turning on fluxes generates a potential for the moduli both in type IIB and in M-theory. We verify that the type IIB analysis gives the same results of the F-theory analysis. In particular, we check that the two potentials match.Comment: 24 pages; reference correcte

Weierstrass meets Enriques

We study in detail the degeneration of K3 to T^4/Z_2. We obtain an explicit embedding of the lattice of collapsed cycles of T^4/Z_2 into the lattice of integral cycles of K3 in two different ways. Our first method exploits the duality to the heterotic string on T^3. This allows us to describe the degeneration in terms of Wilson lines. Our second method is based on the blow-up of T^4/Z_2. From this blow-up, we directly construct the full lattice of integral cycles of K3. Finally, we use our results to describe the action of the Enriques involution on elliptic K3 surfaces, finding that a Weierstrass model description is consistent with the Enriques involution only in the F-theory limit.Comment: 35 pages, 9 figure

G 4 flux, algebraic cycles and complex structure moduli stabilization

We construct G4 fluxes that stabilize all of the 426 complex structure moduli of the sextic Calabi-Yau fourfold at the Fermat point. Studying flux stabilization usually requires solving Picard-Fuchs equations, which becomes unfeasible for models with many moduli. Here, we instead start by considering a specific point in the complex structure moduli space, and look for a flux that fixes us there. We show how to construct such fluxes by using algebraic cycles and analyze flat directions. This is discussed in detail for the sextic Calabi-Yau fourfold at the Fermat point, and we observe that there appears to be tension between M2-tadpole cancellation and the requirement of stabilizing all moduli. Finally, we apply our results to show that even though symmetric fluxes allow to automatically solve several F-term equations, they typically lead to flat directions

Heterotic-Type II duality in the hypermultiplet sector

We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective moduli spaces at the level of the classical effective actions. We determine the parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal form. From the expression of the holomorphic prepotential we are led to conjecture that both X and its mirror must be K3 fibrations in order for the type IIA theory to have an heterotic dual. We then focus on the region of the moduli space where the metric is expressed in terms of a prepotential on both sides of the duality. Applying the duality we derive the heterotic hypermultiplet metric for a gauge bundle which is reduced to 24 point-like instantons. This result is confirmed by using the duality between the heterotic theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on the moduli space of an SU(2) bundle on K3.Comment: 27 pages; references added, typos correcte

On de Sitter string vacua from anti-d3-branes in the large volume scenario

We consider de Sitter vacua realised in concrete type IIB Calabi-Yau compactifications with an anti D3-brane at the tip of a warped throat of Klebanov-Strassler type. The Kähler moduli are stabilised together with the complex structure modulus of the warped throat. The volume is exponentially large as in the large volume scenario (LVS). We analyse the conditions on the parameters of the EFT such that they are in the region of validity of our approximations, there are no runaway problems and the vacua satisfy all consistency constraints, such as tadpole cancellation. We illustrate our results with an explicit Calabi-Yau orientifold with two Kähler moduli and one antibrane on top of an O3-plane in a warped throat, that has the goldstino as its only massless state. The moduli are stabilised with gs∼ 0.2 and volume V∼ 104 in string units, justifying the approximation used to derive the corresponding EFT. Although the model lacks chiral matter, it is presented as a proof of concept, chosen to be the simplest realisation of antibrane uplift

What does inflation really predict?

If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Omega_tot), dark energy (rho_Lambda, w, etc.), the primordial density fluctuations (Omega_tot, dark energy (rho_Lambda, w, etc.). We compute this multivariate probability distribution for various classes of single-field slow-roll models, exploring its dependence on the characteristic inflationary energy scales, the shape of the potential V and and the choice of measure underlying the calculation. We find that unless the characteristic scale Delta-phi on which V varies happens to be near the Planck scale, the only aspect of V that matters observationally is the statistical distribution of its peaks and troughs. For all energy scales and plausible measures considered, we obtain the predictions Omega_tot ~ 1+-0.00001, w=-1 and rho_Lambda in the observed ballpark but uncomfortably high. The high energy limit predicts n_s ~ 0.96, dn_s/dlnk ~ -0.0006, r ~ 0.15 and n_t ~ -0.02, consistent with observational data and indistinguishable from eternal phi^2-inflation. The low-energy limit predicts 5 parameters but prefers larger Q and redder n_s than observed. We discuss the coolness problem, the smoothness problem and the pothole paradox, which severely limit the viable class of models and measures. Our findings bode well for detecting an inflationary gravitational wave signature with future CMB polarization experiments, with the arguably best-motivated single-field models favoring the detectable level r ~ 0.03. (Abridged)Comment: Replaced to match accepted JCAP version. Improved discussion, references. 42 pages, 17 fig

6D Effective Action of Heterotic Compactification on K3 with nontrivial Gauge Bundles

We compute the six-dimensional effective action of the heterotic string compactified on K3 for the standard embedding and for a class of backgrounds with line bundles and appropriate Yang-Mills fluxes. We compute the couplings of the charged scalars and the bundle moduli as functions of the geometrical K3 moduli from a Kaluza-Klein analysis. We derive the D-term potential and show that in the flux backgrounds U(1) vector multiplets become massive by a Stuckelberg mechanism.Comment: 41 pages, typos corrected, references adde

High U(1) charges in type IIB models and their F-theory lift

We construct models with U(1) gauge group and matter with charges up to 6, in the context of type IIB compactifications. We show explicitly that models with charges up to 4 can be derived from corresponding models in F-theory by applying the Sen weak coupling limit. We derive which type IIB models should be the limit of charge 5 and 6 F-theory models. Explicit six dimensional type IIB models with maximal charge 5 and 6 are constructed on an algebraic K3 surface that is the double cover of \u2102\u2119 2 . By using type IIB results we are also able to rediscover the F-theory charge 4 model in a straightforward way