Scattering Equations and String Theory Amplitudes

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for $\alpha'$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results.Comment: v2: 18 pp, 1 figure, added clarifications and comments. Version to be published in PR

Tropical Amplitudes

In this work, we argue that the α′→0 limit of closed string theory scattering amplitudes is a tropical limit. The motivation is to develop a technology to systematize the extraction of Feynman graphs from string theory amplitudes at higher genus. An important technical input from tropical geometry is the use of tropical theta functions with characteristics to rigorously derive the worldline limit of the worldsheet propagator. This enables us to perform a non-trivial computation at two loops: we derive the tropical form of the integrand of the genus-two four-graviton type II string amplitude, which matches the direct field theory computations. At the mathematical level, this limit is an implementation of the correspondence between the moduli space of Riemann surfaces and the tropical moduli space.This research is supported by the Agence Nationale de la Recherche Grant 12-BS05-003-01, from the European Research Council Advanced Grant No. 247252 and from the Centre National de la Recherche Scientifique Grant Projet International de Collaboration Scientifique 6076

Loop Integrands for Scattering Amplitudes from the Riemann Sphere

The scattering equations on the Riemann sphere give rise to remarkable formulae for tree-level gauge theory and gravity amplitudes. Adamo, Casali and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulae, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n-gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.Comment: 5 pages, 1 figure. v3: published versio

An R^4 non-renormalisation theorem in N=4 supergravity

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional N=4 models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of d^2R^4. This implies a non-renormalisation theorem for the R^4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R^4 term to the U(1) anomaly of pure N=4 supergravity.Comment: v2: added comments about one-loop UV divergences. Assorted stylistic corrections. Added references. v3: Eq. III.21 corrected and assorted minor corrections and clarifications. Version to be published. v4: minor corrections. 18 pages. one figur

Controllable adhesion using field-activated fluids

We demonstrate that field-responsive magnetorheological fluids can be used for variable-strength controllable adhesion. The adhesive performance is measured experimentally in tensile tests (a.k.a. probe-tack experiments) in which the magnetic field is provided by a cylindrical permanent magnet. Increasing the magnetic field strength induces higher peak adhesive forces. We hypothesize that the adhesion mechanism arises from the shear resistance of a yield stress fluid in a thin gap. This hypothesis is supported by comparing the experimentally measured adhesive performance to the response predicted by a lubrication model for a non-Newtonian fluid with a field-dependent yield stress. The model predictions are in agreement with experimental data up to moderate field strengths. Above a critical magnetic field strength the model over-predicts the experimentally measured values indicating non-ideal conditions such as local fluid dewetting from the surface.U.S. Army Research Laboratory (United States. Army Research Office Contract/Grant W911NF-08-C-0055

Type I/heterotic duality and M-theory amplitudes

SCOAP

Thermal Transport in Micro- and Nanoscale Systems

Small-scale (micro-/nanoscale) heat transfer has broad and exciting range of applications. Heat transfer at small scale quite naturally is influenced – sometimes dramatically – with high surface area-to-volume ratios. This in effect means that heat transfer in small-scale devices and systems is influenced by surface treatment and surface morphology. Importantly, interfacial dynamic effects are at least non-negligible, and there is a strong potential to engineer the performance of such devices using the progress in micro- and nanomanufacturing technologies. With this motivation, the emphasis here is on heat conduction and convection. The chapter starts with a broad introduction to Boltzmann transport equation which captures the physics of small-scale heat transport, while also outlining the differences between small-scale transport and classical macroscale heat transport. Among applications, examples are thermoelectric and thermal interface materials where micro- and nanofabrication have led to impressive figure of merits and thermal management performance. Basic of phonon transport and its manipulation through nanostructuring materials are discussed in detail. Small-scale single-phase convection and the crucial role it has played in developing the thermal management solutions for the next generation of electronics and energy-harvesting devices are discussed as the next topic. Features of microcooling platforms and physics of optimized thermal transport using microchannel manifold heat sinks are discussed in detail along with a discussion of how such systems also facilitate use of low-grade, waste heat from data centers and photovoltaic modules. Phase change process and their control using surface micro-/nanostructure are discussed next. Among the feature considered, the first are microscale heat pipes where capillary effects play an important role. Next the role of nanostructures in controlling nucleation and mobility of the discrete phase in two-phase processes, such as boiling, condensation, and icing is explained in great detail. Special emphasis is placed on the limitations of current surface and device manufacture technologies while also outlining the potential ways to overcome them. Lastly, the chapter is concluded with a summary and perspective on future trends and, more importantly, the opportunities for new research and applications in this exciting field

Two-loop scattering amplitudes from ambitwistor strings: from genus two to the nodal Riemann sphere

We derive from ambitwistor strings new formulae for two-loop scattering amplitudes in supergravity and super-Yang-Mills theory, with any number of particles. We start by constructing a formula for the type II ambitwistor string amplitudes on a genus-two Riemann surface, and then study the localisation of the moduli space integration on a degenerate limit, where the genus-two surface turns into a Riemann sphere with two nodes. This leads to scattering amplitudes in supergravity, expressed in the formalism of the two-loop scattering equations. For super-Yang-Mills theory, we import `half' of the supergravity result, and determine the colour dependence by considering a current algebra on the nodal Riemann sphere, thereby completely specifying the two-loop analogue of the Parke-Taylor factor, including non-planar contributions. We also present in appendices explicit expressions for the Szego kernels and the partition functions for even spin structures, up to the relevant orders in the degeneration parameters, which may be useful for related investigations in conventional superstring theory.Comment: 66 pages plus appendices, 14 figures. v2: small changes, published version. v3: typos fixed in appendix