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

Minimal Basis for Gauge Theory Amplitudes

Identities based on monodromy for integrations in string theory are used to derive relations between different color ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)! amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.Comment: v2: typos corrected, some rephrasing of the general discussion. Captions to figures added. Version to appear in PRL. 4 pages, 5 figure

Direct Diode Lasers for Industrial Laser Cutting: A Performance Comparison with Conventional Fiber and CO2 Technologies

AbstractThe direct use of diode lasers for cutting sheet metal has high potential to decrease operational costs, but, currently, implementation in industrial environments is constrained by beam quality. In this paper the performance of a novel direct diode laser (DDL) with increased beam quality is documented for both fusion and flame cutting and compared to conventional CO2 and fiber laser sources. Experimental tests were carried out for steel and aluminium based on a Design of Experiments approach. Furthermore, an analytical model, focusing on the absorption of lasers in metals, is described here, which predicts and clarifies performance variation. Although the observed laser beam quality is still lower than the other studied technologies, industrially relevant cutting speeds, with acceptable surface quality, are achievable with DDL, as validated by our result

Two loops in eleven dimensions

The two-loop Feynman diagram contribution to the four-graviton amplitude of eleven-dimensional supergravity compactified on a two-torus, T^2, is analyzed in detail. The Schwinger parameter integrations are re-expressed as integration over the moduli space of a second torus, \hat T^2, which enables the leading low-momentum contribution to be evaluated in terms of maps of \hat T^2 into T^2. The ultraviolet divergences associated with boundaries of moduli space are regularized in a manner that is consistent with the expected duality symmetries of string theory. This leads to an exact expression for terms of order contraction of four Weyl tensors), thereby extending earlier results for the R^4 term that were based on the one-loop eleven-dimensional amplitude. Precise agreement is found with terms in type IIA and IIB superstring theory that arise from the low energy expansion of the tree-level and one-loop string amplitudes and predictions are made for the coefficients of certain two-loop string theory terms as well as for an infinite set of D-instanton contributions. The contribution at the next order in the derivative expansion, \partial^6 R^4, is problematic, which may indicate that it mixes with higher-loop effects in eleven-dimensional supergravity

Classical Observables from the Exponential Representation of the Gravitational S-Matrix

By combining the KMOC-formalism with the exponential representation of the scattering matrix we show that the two-body scattering angle is given by the corresponding matrix element of the exponential representation. This holds to all orders in the Post-Minkowskian expansion of gravity when restricted to the conservative sector. Once gravitational radiation is taken into account new terms correcting this relationship appear starting at fourth Post-Minkowskian order. A systematic expansion of the momentum kick is provided to any order, thus illustrating the iterative structure that partly recycles terms from lower orders in the Post-Minkowskian expansion. We provide explicit results for this computation to fourth Post-Minkowskian order, the first complete calculation at this order based on scattering amplitudes.Comment: 37 pages. v2 : Misprints corrected, text edited, results unchange

String loop corrections to the universal hypermultiplet

We study loop corrections to the universal dilaton supermultiplet for type IIA strings compactified on Calabi-Yau threefolds. We show that the corresponding quaternionic kinetic terms receive non-trivial one-loop contributions proportional to the Euler number of the Calabi-Yau manifold, while the higher-loop corrections can be absorbed by field redefinitions. The corrected metric is no longer Kahler. Our analysis implies in particular that the Calabi-Yau volume is renormalized by loop effects which are present even in higher orders, while there are also one-loop corrections to the Bianchi identities for the NS and RR field strengths.Comment: 30 pages, harvmac, 1 figure. v2: minor typos corrected. Version to appear in Classical and Quantum Gravit

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

Monophyly of the species of Hepatozoon (Adeleorina: Hepatozoidae) parasitizing (African) anurans, with the description of three new species from hyperoliid frogs in South Africa

Haemogregarines (Apicomplexa: Adeleiorina) are a diverse group of haemoparasites reported from almost all vertebrate classes. The most commonly recorded haemogregarines to parasitize anurans are species of Hepatozoon Miller, 1908. To date 16 Hepatozoon species have been described from anurans in Africa, with only a single species, Hepatozoon hyperolli (Hoare, 1932), infecting a member of the Hyperoliidae. Furthermore, only two Hepatozoon species are known from South African anurans, namely Hepatozoon theileri (Laveran, 1905) and Hepatozoon ixoxo Netherlands, Cook and Smit, 2014, from Amietia delalandii (syn. Amietia quecketti) and three Sclerophrys species, respectively. Blood samples were collected from a total of 225 individuals representing nine hyperoliid species from several localities throughout northern KwaZulu-Natal, South Africa. Twenty frogs from three species were found positive for haemogregarines, namely Afrixalus fornasinii (6/14), Hyperolius argus (2/39), and Hyperolius marmoratus (12/74). Based on morphological characteristics, morphometrics and molecular findings three new haemogregarine species, Hepatozoon involucrum Netherlands, Cook and Smit n. sp., Hepatozoon tenuis Netherlands, Cook and Smit n. sp. and Hepatozoon thori Netherlands, Cook and Smit n. sp., are described from hyperoliid hosts. Furthermore, molecular analyses show anuran Hepatozoon species to be a separate monophyletic group, with species isolated from African hosts forming a monophyletic clade within this cluster.Peer reviewe

The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange