436 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
Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
The spinor helicity formalism in four dimensions has become a very useful
tool both for understanding the structure of amplitudes and also for practical
numerical computation of amplitudes. Recently, there has been some discussion
of an extension of this formalism to higher dimensions. We describe a
particular implementation of the spinor-helicity method in ten dimensions.
Using this tool, we study the tree-level S-matrix of ten dimensional super
Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry.
Implications for four-dimensional computations are discussed.Comment: 24 pages, 1 figure
Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
It has been argued in arXiv:1112.6432 that the planar four-point integrand in
N=4 super Yang-Mills theory is uniquely determined by dual conformal invariance
together with the absence of a double pole in the integrand of the logarithm in
the limit as a loop integration variable becomes collinear with an external
momentum. In this paper we reformulate this condition in a simple way in terms
of the amplitude itself, rather than its logarithm, and verify that it holds
for two- and three-loop MHV integrands for n>4. We investigate the extent to
which this collinear constraint and a constraint on the soft behavior of
integrands can be used to determine integrands. We find an interesting
complementarity whereby the soft constraint becomes stronger while the
collinear constraint becomes weaker at larger n. For certain reasonable choices
of basis at two and three loops the two constraints in unison appear strong
enough to determine MHV integrands uniquely for all n.Comment: 27 pages, 14 figures; v2: very minor change
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
Yangian symmetry of light-like Wilson loops
We show that a certain class of light-like Wilson loops exhibits a Yangian
symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops
we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills
theory in a certain kinematical regime. The fact that we find a Yangian
symmetry constraining their functional form can be thought of as the effect of
the original conformal symmetry associated to the scattering amplitudes in the
N=4 theory.Comment: 15 pages, 5 figure
The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
We give an explicit recursive formula for the all L-loop integrand for
scattering amplitudes in N=4 SYM in the planar limit, manifesting the full
Yangian symmetry of the theory. This generalizes the BCFW recursion relation
for tree amplitudes to all loop orders, and extends the Grassmannian duality
for leading singularities to the full amplitude. It also provides a new
physical picture for the meaning of loops, associated with canonical operations
for removing particles in a Yangian-invariant way. Loop amplitudes arise from
the "entangled" removal of pairs of particles, and are naturally presented as
an integral over lines in momentum-twistor space. As expected from manifest
Yangian-invariance, the integrand is given as a sum over non-local terms,
rather than the familiar decomposition in terms of local scalar integrals with
rational coefficients. Knowing the integrands explicitly, it is straightforward
to express them in local forms if desired; this turns out to be done most
naturally using a novel basis of chiral, tensor integrals written in
momentum-twistor space, each of which has unit leading singularities. As simple
illustrative examples, we present a number of new multi-loop results written in
local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise
expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point
3-loop MHV amplitude. The structure of the loop integrand strongly suggests
that the integrals yielding the physical amplitudes are "simple", and
determined by IR-anomalies. We briefly comment on extending these ideas to more
general planar theories.Comment: 46 pages; v2: minor changes, references adde
Holographic dilepton production in a thermalizing plasma
We determine the out-of-equilibrium production rate of dileptons at rest in
strongly coupled N=4 Super Yang-Mills plasma using the AdS/CFT correspondence.
Thermalization is achieved via the gravitational collapse of a thin shell of
matter in AdS_5 space and the subsequent formation of a black hole, which we
describe in a quasistatic approximation. Prior to thermalization, the dilepton
spectral function is observed to oscillate as a function of frequency, but the
amplitude of the oscillations decreases when thermal equilibrium is approached.
At the same time, we follow the flow of the quasinormal spectrum of the
corresponding U(1) vector field towards its equilibrium limit.Comment: 21 pages, 7 figures. v2: Version accepted for publication in JHEP;
minor modifications, added reference
Wilson Loops @ 3-Loops in Special Kinematics
We obtain a compact expression for the octagon MHV amplitude / Wilson loop at
3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed
coefficients. We do this by making use of the cyclic and parity symmetry of the
amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as
in the leading term in the expansion away from this limit. We also make a
natural and quite general assumption about the functional form of the result,
namely that it should consist of weight 6 polylogarithms whose symbol consists
of basic cross-ratios only (and not functions thereof). We also describe the
uplift of this result to 10 points.Comment: 26 pages. Typos correcte
The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
Infrared divergences in scattering amplitudes arise when a loop momentum
becomes collinear with a massless external momentum . In gauge
theories, it is known that the L-loop logarithm of a planar amplitude has much
softer infrared singularities than the L-loop amplitude itself. We argue that
planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected
behavior as already at the level of the integrand. Moreover,
we conjecture that the four-point integrand can be uniquely determined, to any
loop-order, by imposing the correct soft-behavior of the logarithm together
with dual conformal invariance and dihedral symmetry. We use these simple
criteria to determine explicit formulae for the four-point integrand through
seven-loops, finding perfect agreement with previously known results through
five-loops. As an input to this calculation we enumerate all four-point dual
conformally invariant (DCI) integrands through seven-loops, an analysis which
is aided by several graph-theoretic theorems we prove about general DCI
integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive
non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica
files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7
corrected, Lemma 2 remove
Massive amplitudes on the Coulomb branch of N=4 SYM
We initiate a systematic study of amplitudes with massive external particles
on the Coulomb-branch of N=4 super Yang Mills theory: 1) We propose that
(multi-)soft-scalar limits of massless amplitudes at the origin of moduli space
can be used to determine Coulomb-branch amplitudes to leading order in the
mass. This is demonstrated in numerous examples. 2) We find compact explicit
expressions for several towers of tree-level amplitudes, including scattering
of two massive W-bosons with any number of positive helicity gluons, valid for
all values of the mass. 3) We present the general structure of superamplitudes
on the Coulomb branch. For example, the n-point "MHV-band" superamplitude is
proportional to a Grassmann polynomial of mixed degree 4 to 12, which is
uniquely determined by supersymmetry. We find explicit tree-level
superamplitudes for this MHV band and for other simple sectors of the theory.
4) Dual conformal generators are constructed, and we explore the dual conformal
properties of the simplest massive amplitudes. Our compact expressions for
amplitudes and superamplitudes should be of both theoretical and
phenomenological interest; in particular the tree-level results carry over to
truncations of the theory with less supersymmetry.Comment: 29 pages, 1 figur
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