Projectivity of Planar Zeros in Field and String Theory Amplitudes

We study the projective properties of planar zeros of tree-level scattering amplitudes in various theories. Whereas for pure scalar field theories we find that the planar zeros of the five-point amplitude do not enjoy projective invariance, coupling scalars to gauge fields gives rise to tree-level amplitudes whose planar zeros are determined by homogeneous polynomials in the stereographic coordinates labelling the direction of flight of the outgoing particles. In the case of pure gauge theories, this projective structure is generically destroyed if string corrections are taken into account. Scattering amplitudes of two scalars with graviton emission vanish exactly in the planar limit, whereas planar graviton amplitudes are zero for helicity violating configurations. These results are corrected by string effects, computed using the single-valued projection, which render the planar amplitude nonzero. Finally, we discuss how the structure of planar zeros can be derived from the soft limit behavior of the scattering amplitudes.Comment: 39 page, 5 figures. v2: typos corrected. It matches the version published in Journal of High Energy Physic

Temporal disorder in up-down symmetric systems

The effect of temporal disorder on systems with up-down Z2 symmetry is studied. In particular, we analyze two well-known families of phase transitions: the Ising and the generalized voter universality classes, and scrutinize the consequences of placing them under fluctuating global conditions. We observe that variability of the control parameter induces in both classes "Temporal Griffiths Phases" (TGP). These recently-uncovered phases are analogous to standard Griffiths Phases appearing in systems with quenched spatial disorder, but where the roles of space and time are exchanged. TGPs are characterized by broad regions in parameter space in which (i) mean first-passage times scale algebraically with system size, and (ii) the system response (e.g. susceptibility) diverges. Our results confirm that TGPs are quite robust and ubiquitous in the presence of temporal disorder. Possible applications of our results to examples in ecology are discussed

Optimal Carbon Taxes for Emissions Targets in the Electricity Sector

The most dangerous effects of anthropogenic climate change can be mitigated by using emissions taxes or other regulatory interventions to reduce greenhouse gas (GHG) emissions. This paper takes a regulatory viewpoint and describes the Weighted Sum Bisection method to determine the lowest emission tax rate that can reduce the anticipated emissions of the power sector below a prescribed, regulatorily-defined target. This bi-level method accounts for a variety of operating conditions via stochastic programming and remains computationally tractable for realistically large planning test systems, even when binary commitment decisions and multi-period constraints on conventional generators are considered. Case studies on a modified ISO New England test system demonstrate that this method reliably finds the minimum tax rate that meets emissions targets. In addition, it investigates the relationship between system investments and the tax-setting process. Introducing GHG emissions taxes increases the value proposition for investment in new cleaner generation, transmission, and energy efficiency; conversely, investing in these technologies reduces the tax rate required to reach a given emissions target

Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction

In this note we study the applicability of the color-kinematics duality to the scattering of two distinguishable scalar matter particles with gluon emission in QCD, or graviton emission in Einstein gravity. Previous analysis suggested that direct use of the Bern-Carrasco-Johansson double-copy prescription to matter amplitudes does not reproduce the gravitational amplitude in multi-Regge kinematics. This situation, however, can be avoided by extensions to the gauge theory, while maintaning the same Regge limit. Here we present two examples of these extensions: the introduction of a scalar contact interaction and the relaxation of the distinguishability of the scalars. In both cases new diagrams allow for a full reconstruction of the correct Regge limit on the gravitational side. Both modifications correspond to theories obtained by dimensional reduction from higher-dimensional gauge theories.Comment: 16 pages, 1 figure; v2 minor changes, typos corrected. It matches the version published in JHE

Color-kinematics duality and dimensional reduction for graviton emission in Regge limit

In this talk we review the work in [1,2,3] where we have studied the applicability of the color-kinematics duality to the scattering of two distinguishable scalar matter particles with one gluon emission in QCD, or one graviton emission in Einstein gravity. We have shown that the duality works well in the Regge limit under two different extensions of the gauge theory: the introduction of a new scalar contact interaction and the relaxation of the distinguishability of the scalars. Both modifications correspond to theories obtained by dimensional reduction from higher-dimensional pure gauge theories.Comment: 10 pages, no figures. Presented by Agustin Sabio Vera at the Low x workshop, May 30 - June 4 2013, Rehovot and Eilat, Israe