We compare the sets of Calabi-Yau threefolds with large Hodge numbers that are constructed using toric hypersurface methods with those can be constructed as elliptic fibrations using Weierstrass model techniques motivated by F-theory. There is a close correspondence between the structure of "tops" in the toric polytope construction and Tate form tunings of Weierstrass models for elliptic fibrations. We find that all of the Hodge number pairs (h 1,1 , h 2,1 ) with h 1,1 or h 2,1 ≥ 240 that are associated with threefolds in the Kreuzer-Skarke database can be realized explicitly by generic or tuned Weierstrass/Tate models for elliptic fibrations over complex base surfaces. This includes a relatively small number of somewhat exotic constructions, including elliptic fibrations over non-toric bases, models with new Tate tunings that can give rise to exotic matter in the 6D F-theory picture, tunings of gauge groups over non-toric curves, tunings with very large Hodge number shifts and associated nonabelian gauge groups, and tuned Mordell-Weil sections associated with U(1) factors in the corresponding 6D theory. arXiv:1805.05907v6 [hep-th]

We systematically analyze the fibration structure of toric hypersurface Calabi-Yau threefolds with large and small Hodge numbers. We show that there are only four such Calabi-Yau threefolds with h 1,1 ≥ 140 or h 2,1 ≥ 140 that do not have manifest elliptic or genus one fibers arising from a fibration of the associated 4D polytope. There is a genus one fibration whenever either Hodge number is 150 or greater, and an elliptic fibration when either Hodge number is 228 or greater. We find that for small h 1,1 the fraction of polytopes in the KS database that do not have a genus one or elliptic fibration drops exponentially as h 1,1 increases. We also consider the different toric fiber types that arise in the polytopes of elliptic Calabi-Yau threefolds.

We present a simple toy model corresponding to a network of frustrated topological defects of domain walls or cosmic strings that exist previous to the standard slow-roll inflationary era of the universe. Such a network (i) can produce a slower inflationary era than that of the standard scenario if it corresponds to a network of frustrated domain walls or (ii) can induce a vanishing universal acceleration; i.e., the universe would expand at a constant speed, if it corresponds to a network of frustrated cosmic strings. Those features are phenomenologically modeled by a Chaplygin gas that can interpolate between a network of frustrated topological defects and a de Sitter-like or a powerlaw inflationary era. We show that this scenario can alleviate the quadruple anomaly of the cosmic microwave background spectrum. Using the method of the Bogoliubov coefficients, we obtain the spectrum of the gravitational waves as would be measured today for the whole range of frequencies. We comment on the possible detection of this spectrum by the planned detectors like BBO and DECIGO.PACS numbers: 98.80. Bp, 95.36.+x

We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base surface B that supports an elliptic Calabi-Yau threefold has a mirror that is an elliptic fibration over a dual toric base surfaceB that is related through toric geometry to the line bundle −6K B . The Kreuzer-Skarke database includes all these examples and gives a wide range of other more complicated constructions where mirror symmetry also factorizes. Since recent evidence suggests that most Calabi-Yau threefolds are elliptic or genus one fibered, this points to a new way of understanding mirror symmetry that may apply to a large fraction of smooth Calabi-Yau threefolds. The factorization structure identified here can also apply for Calabi-Yau manifolds of higher dimension.A The 16 reflexive 2D fiber polytopes ∇ 2 26 B Faces of the base polytope and chains of non-Higgsable clusters 26 the G2 has one additional fundamental (7), which contributes another 6 hypermultiplets charged under the Cartan, canceling the difference in dimension between SU (2) and G2. This rank-preserving tuning between SU (2) and G2 connects two phases of the same Calabi-Yau geometry. 11 Additional vertices from tops for all generic fibrations over Hirzebruch surfaces can be looked up in Table 11 in [15].

Light absorption is a common phenomenon in nature, but accurate and quantitative absorption measurement at the nanoscale remains challenging especially in the application of widefield imaging. Here, we demonstrated optical widefield interferometric photothermal microscopy that allowed us to visualize and quantify the heat generation of single nanoparticles. The working principle was to measure the scattering signal due to the refractive index change of the surrounding media induced by the dissipated heat (known as the thermal lens effect). The sensitivity of our local heat measurement was a few nanowattsthe high sensitivity made it possible to detect single gold nanoparticles, as small as 5 nm. By changing the particle sizes, we found that, for small metallic nanoparticles (gold and silver nanoparticles < 40 nm), the photothermal signal was determined by the amount of the dissipated heat, independent of the particle size. A model was established to explain our experimental results, indicating that the photothermal signal was essentially contributed by the interferometric detection of the scattered field of the thermal lens. Importantly, on the basis of this model, we further investigated the photothermal signal of large nanoparticles (40–100 nm for our setup) where the scattered light of the particle was considerable relative to the probe light. In this regime, the strong scattered field of the particle effectively served as the main reference beam that interfered with the scattered field of the thermal lens, resulting in an enhanced photothermal signal. Our work illustrates an important fact that the measured photothermal signal is fundamentally affected by the scattering property of the sample. This finding paves the way to accurate and sensitive absorption-based imaging in complex biological samples where the scattering is often spatially heterogeneous.