21 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
From Polygon Wilson Loops to Spin Chains and Back
Null Polygon Wilson Loops (WL) in N=4 SYM can be computed using the Operator
Product Expansion in terms of a transition amplitude on top of a color flux
tube (FT). That picture is valid at any value of the 't Hooft coupling. So far
it has been efficiently used at weak coupling (WC) in cases where only a single
particle is flowing. At any finite value of the coupling however, an infinite
number of particles are flowing on top of the color FT. A major open problem in
this approach was how to deal with generic multi-particle states at WC. In this
paper we study the propagation of any number of FT excitations at WC. We do
this by first mapping the WL into a sum of two point functions of local
operators. This map allows us to translate the integrability techniques
developed for the spectrum problem back to the WL. E.g., the FT Hamiltonian can
be represented as a simple kernel acting on the loop. Having an explicit
representation for the FT Hamiltonian allows us to treat any number of
particles on an equal footing. We use it to bootstrap some simple cases where
two particles are flowing, dual to N2MHV amplitudes. The FT is integrable and
therefore has other (infinite set of) conserved charges. The generating
function of conserved charges is constructed from the monodromy (M) matrix
between sides of the polygon. We compute it for some simple examples at leading
order at WC. At strong coupling (SC), these Ms were the main ingredients of the
Y-system solution. To connect the WC and SC computations, we study a case where
an infinite number of particles are propagating already at leading order at WC.
We obtain a precise match between the WC and SC Ms. That match is the WL
analogue of the well known Frolov-Tseytlin limit where the WC and SC
descriptions become identical. Hopefully, putting the WC and SC descriptions on
the same footing is the first step in understanding the all loop structure.Comment: 52 pages, 14 figures, the abstract in the pdf is not encrypted and is
slightly more detaile