232 research outputs found
Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
The resummation of soft gluon exchange for QCD hard scattering requires a
matrix of anomalous dimensions, which has been computed through two loops. The
two-loop matrix is proportional to the one-loop matrix. Recently there have
been proposals that this proportionality extends to higher loops. One can test
such proposals by computing the dependence of this matrix on the matter content
in a generic gauge theory. It is shown that for the matter-dependent part the
proportionality extends to three loops for arbitrary massless processes.Comment: 5 pages, 2 figures; v2 minor clarifications, references adde
Twistor String Theory and QCD
I review recent progress in using twistor-inspired methods to compute
perturbative scattering amplitudes in gauge theory, for application to collider
physics.Comment: 17 pages, 9 figures. Presented at the International Europhysics
Conference on High Energy Physics (Lisbon, July, 2005
The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
We use the principle of maximal transcendentality and the universal nature of
subleading infrared poles to extract the analytic value of the four-loop
collinear anomalous dimension in planar super-Yang-Mills theory
from recent QCD results, obtaining . This value agrees with a previous
numerical result to within 0.2 percent. It also provides the Regge trajectory,
threshold soft anomalous dimension and rapidity anomalous dimension through
four loops.Comment: 12 pages, no figures. v2, references adde
Ultraviolet Behavior of N=8 Supergravity
In these lectures I describe the remarkable ultraviolet behavior of N=8
supergravity, which through four loops is no worse than that of N=4
super-Yang-Mills theory (a finite theory). I also explain the computational
tools that allow multi-loop amplitudes to be evaluated in this theory - the KLT
relations and the unitarity method - and sketch how ultraviolet divergences are
extracted from the amplitudes.Comment: 30 pages, 12 figures; lectures presented at International School of
Subnuclear Physics, 47th Course, Erice Sicily, August 29-September 7, 200
Recent Developments in Perturbative QCD
I review recent progress in perturbative QCD on two fronts: extending
next-to-next-to-leading order QCD corrections to a broader range of collider
processes, and applying twistor-space methods (and related spinoffs) to
computations of multi-parton scattering amplitudes.Comment: 13 pages, 7 figures. Talk presented at 13th International Workshop on
Deep Inelastic Scattering (DIS 05), Madison, Wisconsin, April, 200
Gluing Ladders into Fishnets
We use integrability at weak coupling to compute fishnet diagrams for
four-point correlation functions in planar theory. The results are
always multi-linear combinations of ladder integrals, which are in turn built
out of classical polylogarithms. The Steinmann relations provide a powerful
constraint on such linear combinations, leading to a natural conjecture for any
fishnet diagram as the determinant of a matrix of ladder integrals.Comment: 6 pages, 4 figures; v2, minor corrrections, e.g. in fig. 2 captio
Bootstrapping an NMHV amplitude through three loops
We extend the hexagon function bootstrap to the
next-to-maximally-helicity-violating (NMHV) configuration for six-point
scattering in planar super-Yang-Mills theory at three loops.
Constraints from the differential equation, from the operator product
expansion (OPE) for Wilson loops with operator insertions, and from multi-Regge
factorization, lead to a unique answer for the three-loop ratio function. The
three-loop result also predicts additional terms in the OPE expansion, as well
as the behavior of NMHV amplitudes in the multi-Regge limit at one higher
logarithmic accuracy (NNLL) than was used as input. Both predictions are in
agreement with recent results from the flux-tube approach. We also study the
multi-particle factorization of multi-loop amplitudes for the first time. We
find that the function controlling this factorization is purely logarithmic
through three loops. We show that a function , which is closely related to
the parity-even part of the ratio function , is remarkably simple; only five
of the nine possible final entries in its symbol are non-vanishing. We study
the analytic and numerical behavior of both the parity-even and parity-odd
parts of the ratio function on simple lines traversing the space of cross
ratios , as well as on a few two-dimensional planes. Finally, we
present an empirical formula for in terms of elements of the coproduct of
the six-gluon MHV remainder function at one higher loop, which works
through three loops for (four loops for ).Comment: 69 pages, 12 figures, 1 table, 3 ancillary files; v2, minor typo's
correcte
Universal structure of subleading infrared poles in gauge theory amplitudes
We study the origin of subleading soft and collinear poles of form factors
and amplitudes in dimensionally-regulated massless gauge theories. In the case
of form factors of fundamental fields, these poles originate from a single
function of the coupling, denoted G(alpha_s), depending on both the spin and
gauge quantum numbers of the field. We relate G(alpha_s) to gauge-theory matrix
elements involving the gluon field strength. We then show that G(alpha_s) is
the sum of three terms: a universal eikonal anomalous dimension, a universal
non-eikonal contribution, given by the coefficient B_delta (alpha_s) of delta(1
- z) in the collinear evolution kernel, and a process-dependent short-distance
coefficient function, which does not contribute to infrared poles. Using
general results on the factorization of soft and collinear singularities in
fixed-angle massless gauge theory amplitudes, we conclude that all such
singularities are captured by the eikonal approximation, supplemented only by
the knowledge of B_delta (alpha_s). We explore the consequences of our results
for conformal gauge theories, where in particular we find a simple exact
relation between the form factor and the cusp anomalous dimension.Comment: 29 pages, 1 figure; version published on JHEP, two added reference
Gluon scattering in N=4 super-Yang-Mills theory from weak to strong coupling
I describe some recent developments in the understanding of gluon scattering
amplitudes in N=4 super-Yang-Mills theory in the large-N_c limit. These
amplitudes can be computed to high orders in the weak coupling expansion, and
also now at strong coupling using the AdS/CFT correspondence. They hold the
promise of being solvable to all orders in the gauge coupling, with the help of
techniques based on integrability. They are intimately related to expectation
values for polygonal Wilson loops composed of light-like segments.Comment: 20 pages, 10 figures, talk presented at RADCOR 200
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