Amplitudes at Infinity

We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to demonstrate the absence of poles at infinity of all MHV amplitudes through three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads us to discover that this theory does support non-vanishing residues at infinity starting at two loops, and the degree of these poles grow arbitrarily with multiplicity. This causes a tension between simultaneously manifesting ultraviolet finiteness---which would be automatic in a representation obtained by color-kinematic duality---and gauge invariance---which would follow from unitarity-based methods.Comment: 4+1+1 pages; 15 figures; details provided in ancillary Mathematica file

On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

We present evidence that loop amplitudes in maximally supersymmetric $\mathcal{N}=4$ Yang-Mills (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full $\mathcal{N}=4$ SYM has only logarithmic singularities and is free of any poles at infinity---properties closely related to uniform transcendentality and the UV-finiteness of the theory. We also briefly comment on implications for maximal ($\mathcal{N}=8$) supergravity.Comment: 4 pages, 3 figure

On-Shell Structures of MHV Amplitudes Beyond the Planar Limit

We initiate an exploration of on-shell functions in $\mathcal{N}=4$ SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. This is understood in terms of an extended notion of positivity in $G(2,n)$, the Grassmannian of 2-planes in $n$ dimensions: a single on-shell diagram can be associated with many different "positive" regions, of which the familiar positive region associated with planar diagrams is just one example. The decomposition into Parke-Taylor factors is simply a "triangulation" of these extended positive regions. The $U(1)$ decoupling and Kleiss-Kuijf (KK) relations satisfied by the Parke-Taylor amplitudes also follow naturally from this geometric picture. These results suggest that non-planar MHV amplitudes in $\mathcal{N}=4$ SYM at all loop orders can be expressed as a sum of polylogarithms weighted by color factors and (unordered) Parke-Taylor amplitudes.Comment: 16 pages, 19 figure

Prescriptive Unitarity

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N^kMHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions

High energy constraints in the octet SS-PP correlator and resonance saturation at NLO in 1/Nc

We study the octet SS-PP correlator within resonance chiral theory up to the one-loop level, i.e., up to next-to-leading order in the 1/Nc expansion. We will require that our correlator follows the power behaviour prescribed by the operator product expansion at high euclidian momentum. Nevertheless, we will not make use of short-distance constraints from other observables. Likewise, the high-energy behaviour will be demanded for the whole correlator, not for individual absorptive channels. The amplitude is progressively improved by considering more and more complicated operators in the hadronic lagrangian. Matching the resonance chiral theory result with chiral perturbation theory at low energies produces the estimates L_8(mu)^{SU(3)} = (1.0+-0.4)10^-3 and C_{38}(mu)^{SU(3)} = (8+-5) 10^-6 for mu=770 MeV. The effect of alternative renormalization schemes is also discussed in the article.Comment: 40 pages, 18 figure

Interactively modelling land profitability to estimate European agricultural and forest land use under future scenarios of climate, socio-economics and adaptation

Studies of climate change impacts on agricultural land use generally consider sets of climates combined with fixed socio-economic scenarios, making it impossible to compare the impact of specific factors within these scenario sets. Analysis of the impact of specific scenario factors is extremely difficult due to prohibitively long run-times of the complex models. This study produces and combines metamodels of crop and forest yields and farm profit, derived from previously developed very complex models, to enable prediction of European land use under any set of climate and socio-economic data. Land use is predicted based on the profitability of the alternatives on every soil within every 10' grid across the EU. A clustering procedure reduces 23,871 grids with 20+ soils per grid to 6,714 clusters of common soil and climate. Combined these reduce runtime 100 thousand-fold. Profit thresholds define land as intensive agriculture (arable or grassland), extensive agriculture or managed forest, or finally unmanaged forest or abandoned land. The demand for food as a function of population, imports, food preferences and bioenergy, is a production constraint, as is irrigation water available. An iteration adjusts prices to meet these constraints. A range of measures are derived at 10' grid-level such as diversity as well as overall EU production. There are many ways to utilise this ability to do rapidWhat-If analysis of both impact and adaptations. The paper illustrates using two of the 5 different GCMs (CSMK3, HADGEM with contrasting precipitation and temperature) and two of the 4 different socio-economic scenarios ("We are the world", "Should I stay or should I go" which have contrasting demands for land), exploring these using two of the 13 scenario parameters (crop breeding for yield and population) . In the first scenario, population can be increased by a large amount showing that food security is far from vulnerable. In the second scenario increasing crop yield shows that it improves the food security problem

Building Bases of Loop Integrands

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all `leading-(transcendental-)weight' contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory---for generic helicities and arbitrary multiplicity.Comment: 76 pages, 6 tables, hundreds of figures. Ancillary file includes our results for three loop

Liquid droplet formation by HP1α suggests a role for phase separation in heterochromatin.

Gene silencing by heterochromatin is proposed to occur in part as a result of the ability of heterochromatin protein 1 (HP1) proteins to spread across large regions of the genome, compact the underlying chromatin and recruit diverse ligands. Here we identify a new property of the human HP1α protein: the ability to form phase-separated droplets. While unmodified HP1α is soluble, either phosphorylation of its N-terminal extension or DNA binding promotes the formation of phase-separated droplets. Phosphorylation-driven phase separation can be promoted or reversed by specific HP1α ligands. Known components of heterochromatin such as nucleosomes and DNA preferentially partition into the HP1α droplets, but molecules such as the transcription factor TFIIB show no preference. Using a single-molecule DNA curtain assay, we find that both unmodified and phosphorylated HP1α induce rapid compaction of DNA strands into puncta, although with different characteristics. We show by direct protein delivery into mammalian cells that an HP1α mutant incapable of phase separation in vitro forms smaller and fewer nuclear puncta than phosphorylated HP1α. These findings suggest that heterochromatin-mediated gene silencing may occur in part through sequestration of compacted chromatin in phase-separated HP1 droplets, which are dissolved or formed by specific ligands on the basis of nuclear context