1,444 research outputs found
Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
We show that scattering amplitudes in planar N = 4 Super Yang-Mills in
multi-Regge kinematics can naturally be expressed in terms of single-valued
iterated integrals on the moduli space of Riemann spheres with marked points.
As a consequence, scattering amplitudes in this limit can be expressed as
convolutions that can easily be computed using Stokes' theorem. We apply this
framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove
that at L loops all MHV amplitudes are determined by amplitudes with up to L +
4 external legs. We also investigate non-MHV amplitudes, and we show that they
can be obtained by convoluting the MHV results with a certain helicity flip
kernel. We classify all leading singularities that appear at LLA in the Regge
limit for arbitrary helicity configurations and any number of external legs.
Finally, we use our new framework to obtain explicit analytic results at LLA
for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to
eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the
results in Mathematica forma
On the breaking of collinear factorization in QCD
We investigate the breakdown of collinear factorization for non-inclusive
observables in hadron-hadron collisions. For pure QCD processes, factorization
is violated at the three-loop level and it has a structure identical to that
encountered previously in the case of super-leading logarithms. In particular,
it is driven by the non-commutation of Coulomb/Glauber gluon exchanges with
other soft exchanges. Beyond QCD, factorization may be violated at the two-loop
level provided that the hard subprocess contains matrix element contributions
with phase differences between different colour topologies.Comment: Version 2: minor improvements for journal publicatio
The non-Abelian gauge theory of matrix big bangs
We study at the classical and quantum mechanical level the time-dependent
Yang-Mills theory that one obtains via the generalisation of discrete
light-cone quantisation to singular homogeneous plane waves. The non-Abelian
nature of this theory is known to be important for physics near the
singularity, at least as far as the number of degrees of freedom is concerned.
We will show that the quartic interaction is always subleading as one
approaches the singularity and that close enough to t=0 the evolution is driven
by the diverging tachyonic mass term. The evolution towards asymptotically flat
space-time also reveals some surprising features.Comment: 29 pages, 8 eps figures, v2: minor changes, references added: v3
small typographical changes
Curvature formula for the space of 2-d conformal field theories
We derive a formula for the curvature tensor of the natural Riemannian metric
on the space of two-dimensional conformal field theories and also a formula for
the curvature tensor of the space of boundary conformal field theories.Comment: 36 pages, 1 figure; v2 references adde
Differential equations for multi-loop integrals and two-dimensional kinematics
In this paper we consider multi-loop integrals appearing in MHV scattering
amplitudes of planar N=4 SYM. Through particular differential operators which
reduce the loop order by one, we present explicit equations for the two-loop
eight-point finite diagrams which relate them to massive hexagons. After the
reduction to two-dimensional kinematics, we solve them using symbol technology.
The terms invisible to the symbols are found through boundary conditions coming
from double soft limits. These equations are valid at all-loop order for double
pentaladders and allow to solve iteratively loop integrals given lower-loop
information. Comments are made about multi-leg and multi-loop integrals which
can appear in this special kinematics. The main motivation of this
investigation is to get a deeper understanding of these tools in this
configuration, as well as for their application in general four-dimensional
kinematics and to less supersymmetric theories.Comment: 25 pages, 7 figure
Limits of minimal models and continuous orbifolds
The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be
equivalent to the singlet sector of a free boson theory, thus paralleling
exactly the structure of the free theory in the Klebanov-Polyakov proposal. In
2d, the singlet sector does not describe a consistent theory by itself since
the corresponding partition function is not modular invariant. However, it can
be interpreted as the untwisted sector of a continuous orbifold, and this point
of view suggests that it can be made consistent by adding in the appropriate
twisted sectors. We show that these twisted sectors account for the `light
states' that were not included in the original 't Hooft limit. We also show
that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold
agrees precisely with the limit theory of Runkel & Watts. In particular, this
implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published
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