29 research outputs found
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 SYM theory
We present numerical results for the nonplanar lightlike cusp and collinear
anomalous dimension at four loops in 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