Hyperinflation generalised: from its attractor mechanism to its tension with the `swampland conjectures'

In negatively curved field spaces, inflation can be realised even in steep potentials. Hyperinflation invokes the `centrifugal force' of a field orbiting the hyperbolic plane to sustain inflation. We generalise hyperinflation by showing that it can be realised in models with any number of fields ($N_f\geq2$), and in broad classes of potentials that, in particular, don't need to be rotationally symmetric. For example, hyperinflation can follow a period of radial slow-roll inflation that undergoes geometric destabilisation, yet this inflationary phase is not identical to the recently proposed scenario of `side-tracked inflation'. We furthermore provide a detailed proof of the attractor mechanism of (the original and generalised) hyperinflation, and provide a novel set of characteristic, explicit models. We close by discussing the compatibility of hyperinflation with observations and the recently much discussed `swampland conjectures'. Observationally viable models can be realised that satisfy either the `de Sitter conjecture' ($V'/V\gtrsim 1$) or the `distance conjecture' ($\Delta \phi \lesssim 1$), but satisfying both simultaneously brings hyperinflation in some tension with successful reheating after inflation. However, hyperinflation can get much closer to satisfying all of these criteria than standard slow-roll inflation. Furthermore, while the original model is in stark tension with the weak gravity conjecture, generalisations can circumvent this issue.Comment: 26 pages, 3 figure

All tree-level amplitudes in massless QCD

We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N=4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N=4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N=4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark-pairs.Comment: 40 pages, Mathematica package GGT.m and example notebook is included in submission, v2: QCD four fermion line translations provided; GGT version 1.1 update with a numerical evaluation function; comments on computer speed optimizations, v3: Minor changes, version to be published in JHEP, v4: published version in JHE

Scattering into the fifth dimension of N=4 super Yang-Mills

We study an alternative to dimensional regularisation of planar scattering amplitudes in N=4 super Yang-Mills theory by going to the Coulomb phase of the theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism, allowing us to work in four dimensions. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. The latter acts on the kinematical variables of the amplitudes as well as on the Higgs masses in an effectively five dimensional space. We confirm this expectation by an explicit calculation in the gauge theory. A consequence of this exact dual conformal symmetry is a significantly reduced set of scalar basis integrals that are allowed to appear in an amplitude. For example, triangle sub-graphs are ruled out. We argue that the study of exponentiation of amplitudes is simpler in the Higgsed theory because evanescent terms in the mass regulator can be consistently dropped. We illustrate this by showing the exponentiation of a four-point amplitude to two loops. Finally, we also analytically compute the small mass expansion of a two-loop master integral with an internal mass.Comment: 35 pages, many figures. v2: typos and references fixed. v3: minor changes, version to be published in JHE

Synthesis and C−C Coupling Reactivity of a Dinuclear Ni^I−Ni^I Complex Supported by a Terphenyl Diphosphine

Mono- and bimetallic complexes of nickel supported by a terphenyl diphosphine have been synthesized. The reported complexes show diverse metal−arene interactions in the solid state. Reactions of an o,o′-biphenyldiyl dinickel complex with CO and dichloroalkanes lead to fluorene derivatives, indicating the formation of carbon−carbon bonds at a bimetallic moiety

Zirconium and titanium complexes supported by tridentate LX2 ligands having two phenolates linked to furan, thiophene, and pyridine donors: precatalysts for propylene polymerization and oligomerization

Zirconium and titanium complexes with tridentate bis(phenolate)-donor (donor = pyridine, furan and thiophene) ligands have been prepared and investigated for applications in propylene polymerization. The ligand framework has two X-type phenolates connected to the flat heterocyclic L-type donor at the 2,6- or 2.5- positions via direct ring-ring (sp^2-sp^2)linkages. The zirconium and titanium dibenzyl complexes have been prepared by treatment of the neutral bis(phenol)-donor ligands with M(CH_2Ph)_4 (M = Ti, Zr) with loss of 2 equiv of toluene. Titanium complexes with bis(phenolate)pyridine and -furan ligands and zirconium complexes with bis(phenolate)pyridine and -thiophene ligands have been characterized by single-crystal X-ray diffraction. The solid-state structures of the bis(benzyl)titanium complexes are roughly C_2 symmetric, while the zirconium derivatives display C_s and C^1 symmetry. The bis(phenolate)pyridine titanium complexes are structurally affected by the size of the substituents substituents (CMe_3 or CEt_3) ortho to the oxygens, the larger group leading to a larger C_2 distortion. Both titanium and zirconium dibenzyl complexes were found to be catalyst precursors for the polymerization of propylene upon activation with methylaluminoxane (MAO). The activities observed for the zirconium complexes are particularly notable, exceeding 10^6 g polypropylene/mol Zr center dot h in some cases. The bis(phenolate)pyridine titanium analogues are about 10^3 times less active, but generate polymers of higher molecular weight. When activated with MAO, the titanium bis(phenolate)furan and bis(phenolate)thiophene systems were found to promote propylene oligomerization