Maximal R-symmetry violating amplitudes in type IIB superstring theory

On-shell superspace techniques are used to quantify R-symmetry violation in type IIB superstring theory amplitudes in a flat background in ten dimensions. This shows the existence of a particularly simple class of non-vanishing amplitudes in this theory which violate R-symmetry maximally. General properties of the class and some of its extensions are established which at string tree level are shown to determine the first three non-trivial effective field theory contributions to all multiplicity. This leads to a natural conjecture for the exact analytic part of the first two of these.Comment: 10 pages. minute modifications, references adde

String theory in target space

It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are (generalised) Britto-Cachazo-Feng-Witten shifts, as well as the monodromy relations for open string theory and the Kawai-Lewellen-Tye relations for closed string theory. The roots of the scattering amplitudes and especially their appearance in the residues at the kinematic poles are central to the story. These residues determine the amplitudes through on-shell recursion relations. Several checks of the formalism are presented, including a computation of the Koba-Nielsen amplitude in the bosonic string. Furthermore the question of target space unitarity is (re-)investigated. For the Veneziano amplitude this question is reduced by Poincare invariance, unitarity and locality to that of positivity of a particular numerical sum. Interestingly, this analysis produces the main conditions of the no-ghost theorem on dimension and intercept from the first three poles of this amplitude.Comment: 66 pages, many figure

A minimal approach to the scattering of physical massless bosons

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A range of proof-of-concept examples is presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control color quantum numbers of scattering amplitudes with matter.Comment: 65 pages, exposition improved, typos correcte

The nonplanar cusp and collinear anomalous dimension at four loops in N=4{\mathcal N} = 4 SYM theory

We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in ${\mathcal N} = 4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear combination of uniformly transcendental integrals for arbitrary colour factor. Numerical integration in the nonplanar sector reveals explicitly the breakdown of quadratic Casimir scaling at the four-loop order. A thorough analysis of the reported numerical uncertainties is carried out.Comment: 10 pages, 2 figures, 1 table. Proceedings of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austri

The Sudakov form factor at four loops in maximal super Yang-Mills theory

The four-loop Sudakov form factor in maximal super Yang-Mills theory is analysed in detail. It is shown explicitly how to construct a basis of integrals that have a uniformly transcendental expansion in the dimensional regularisation parameter, further elucidating the number-theoretic properties of Feynman integrals. The physical form factor is expressed in this basis for arbitrary colour factor. In the nonplanar sector the required integrals are integrated numerically using a mix of sector-decomposition and Mellin-Barnes representation methods. Both the cusp as well as the collinear anomalous dimension are computed. The results show explicitly the violation of quadratic Casimir scaling at the four-loop order. A thorough analysis concerning the reliability of reported numerical uncertainties is carried out.Comment: 47 pages, 17 figures; v4: fixed typo in eqs. (4.4) and (A.4), final result unchange