Worldsheet instantons,torsion curves and non-perturbative superpotentials

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov–Witten invariants for a Calabi–Yau threefold with fundamental group π₁(X)=Z₃×Z₃${\pi }_1(X)={\mathbb{Z}}_3\times {\mathbb{Z}}_3$. We find that the curves fall into homology classes in H₂(X,Z)=Z³⊕(Z₃⊕Z₃)$H_2(X,\mathbb{Z})={\mathbb{Z}}^3\oplus ({\mathbb{Z}}_3\oplus {\mathbb{Z}}_3)$. The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov–Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.     

Probing the out-of-plane distortion of single point defects in atomically thin hexagonal boron nitride at the picometer scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride (h-BN) accompanied by first-principles calculations reveals a characteristic charge-induced pm symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer h-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the h-BN membrane.     

A study of fused silica micro/nano patterning by focused-ion-beam

A dual-beam scanning electron microscopy (SEM)/focused-ion-beam (FIB) system was used to pattern fused silica substrates coated with a 15 nm thin Cr layer. The dimensions of fabricated features together with their surface morphology and profiles were investigated by SEM and atomic force microscopy (AFM). The study demonstrated that with the increase of the ion beam fluence the sputtering rate of the fused silica decreased non-linearly. Also, it was found that initially the sputtering rate increased with the increase of the beam current, after reaching a maximum value, it started decreasing when further beam current increment was performed. Compared with unprocessed areas, the surface finish of the features fabricated by FIB exhibited a significant improvement, and the ion fluence influence on the surface roughness of trenches with low aspect ratios could be considered as negligible. Using a fine beam probe, nano-gratings in the form of grooves with a width down to 54 nm and an aspect ratio higher than three were fabricated. The study showed that FIB machining could be an alternative technology to e-beam lithography for producing fused silica templates for UV nanoimprinting.     

Patterning of amorphous and polycrystalline Ni78B14Si8 with a focused-ion-beam

The machining response of amorphous and crystalline Ni₇₈B₁₄Si₈ was investigated when structuring substrates using focused-ion-beam (FIB) milling. In particular, the sputtering yield as a function of the scan speed, and the effects of ion fluence and scan speed on the milled depth were studied. The ion fluence dependent evolution of the cross-sectional profiles of trenches was examined by atomic force microscopy (AFM). When milling amorphous Ni₇₈B₁₄Si₈, it was found that the sputtering yield first decreased with increasing the beam scan speed, then kept constant within the scan speed range, up to 710 nm/s, investigated in this work; it was also found that the milled depth was almost proportional to the ion beam fluence. The patterning of polycrystalline Ni₇₈B₁₄Si₈ resulted in anisotropic milling-rates due to the varying orientation of the grains in the material. The analysis of the profile evolution in both materials indicated that the surface finish of trenches was scan speed, ion beam fluence and scan strategy dependent. The study demonstrated that direct patterning by FIB could be used for producing masters in amorphous Ni-based alloys for injection moulding and hot embossing.     

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ? Q² ? 16 GeV². Excellent agreement is obtained using $\text{g}{}^2\text{(2}\text{GeV}\text{)}\text{4π}{}^2\text{= 0.17}$ for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of $\text{M}{}_0{}^2\text{Q}{}^2$. We use data from the resonance region to show $\text{M}{}_0\text{? 400}\text{MeV}$, in agreement with theoretical expectations. Our fit to νW₂ in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of $\text{R =}\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ at large x and Q² are systematically higher than our predictions.     

Bistriazoles Connected Through a B−B Bridge,Synthesized by Highly Selective Dipolar Cycloaddition Reactions of a Diazido-diborane(4)

In this work we report the first cycloaddition reactions between a diazido diborane(4) and terminal alkynes, providing unique access to bis-1,2,3-triazoles connected by a B−B bridge. The catalyst-free reactions are highly selective, yielding exclusively the thermodynamically disfavored bis-1,4-triazoles. The reactions are enabled by the high thermal stability of the diazido-diborane [B(hpp)(N₃)]₂ (hpp=1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-α]pyrimidinate). Due to the tetra-coordinate boron atoms in this reagent, the reactions are tolerant with respect to the introduction of Lewis-basic groups at the alkyne. The scope and limitations of the new reactions are discussed.