23 research outputs found
Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
We argue that the scattering amplitudes in the maximally supersymmetric N=4
super-Yang-Mills theory possess a new symmetry which extends the previously
discovered dual conformal symmetry. To reveal this property we formulate the
scattering amplitudes as functions in the appropriate dual superspace.
Rewritten in this form, all tree-level MHV and next-to-MHV amplitudes exhibit
manifest dual superconformal symmetry. We propose a new, compact and Lorentz
covariant formula for the tree-level NMHV amplitudes for arbitrary numbers and
types of external particles. The dual conformal symmetry is broken at loop
level by infrared divergences. However, we provide evidence that the anomalous
contribution to the MHV and NMHV superamplitudes is the same and, therefore,
their ratio is a dual conformal invariant function. We identify this function
by an explicit calculation of the six-particle amplitudes at one loop. We
conjecture that these properties hold for all, MHV and non-MHV, superamplitudes
in N=4 SYM both at weak and at strong coupling.Comment: 58 page
The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate
the hexagonal light-like Wilson loop at two loops in N=4 super Yang-Mills
theory. We compare its finite part to the Bern-Dixon-Smirnov (BDS) conjecture
for the finite part of the six-gluon amplitude. We find that the two
expressions have the same behavior in the collinear limit, but they differ by a
non-trivial function of the three (dual) conformally invariant variables. This
implies that either the BDS conjecture or the gluon amplitude/Wilson loop
duality fails for the six-gluon amplitude, starting from two loops. Our results
are in qualitative agreement with the analysis of Alday and Maldacena of
scattering amplitudes with infinitely many external gluons.Comment: 8 pages, 3 figures; typos correcte
Generalized unitarity for N=4 super-amplitudes
We develop a manifestly supersymmetric version of the generalized unitarity
cut method for calculating scattering amplitudes in N=4 SYM theory. We
illustrate the power of this method by computing the one-loop n-point NMHV
super-amplitudes. The result confirms two conjectures which we made in
arXiv:0807.1095 [hep-th]. Firstly, we derive the compact, manifestly dual
superconformally covariant form of the NMHV tree amplitudes for arbitrary
number and types of external particles. Secondly, we show that the ratio of the
one-loop NMHV to the MHV amplitude is dual conformal invariant.Comment: 41 pages, 9 figure
One-loop derivation of the Wilson polygon - MHV amplitude duality
We discuss the origin of the Wilson polygon - MHV amplitude duality at the
perturbative level. It is shown that the duality for the MHV amplitudes at
one-loop level can be proven upon the peculiar change of variables in Feynman
parametrization and the use of the relation between Feynman integrals at the
different space-time dimensions. Some generalization of the duality which
implies the insertion of the particular vertex operator at the Wilson triangle
is found for the 3-point function. We discuss analytical structure of Wilson
loop diagrams and present the corresponding Landau equations. The geometrical
interpretation of the loop diagram in terms of the hyperbolic geometry is
discussed.Comment: 29 page
Hidden Simplicity of Gauge Theory Amplitudes
These notes were given as lectures at the CERN Winter School on Supergravity,
Strings and Gauge Theory 2010. We describe the structure of scattering
amplitudes in gauge theories, focussing on the maximally supersymmetric theory
to highlight the hidden symmetries which appear. Using the BCFW recursion
relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory,
and describe how it produces a sum of invariants of a large symmetry algebra.
We review amplitudes in the planar theory beyond tree-level, describing the
connection between amplitudes and Wilson loops, and discuss the implications of
the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe
Generic multiloop methods and application to N=4 super-Yang-Mills
We review some recent additions to the tool-chest of techniques for finding
compact integrand representations of multiloop gauge-theory amplitudes -
including non-planar contributions - applicable for N=4 super-Yang-Mills in
four and higher dimensions, as well as for theories with less supersymmetry. We
discuss a general organization of amplitudes in terms of purely cubic graphs,
review the method of maximal cuts, as well as some special D-dimensional
recursive cuts, and conclude by describing the efficient organization of
amplitudes resulting from the conjectured duality between color and kinematic
structures on constituent graphs.Comment: 42 pages, 18 figures, invited review for a special issue of Journal
of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2 minor
corrections, v3 added reference
Amplitudes at Weak Coupling as Polytopes in AdS_5
We show that one-loop scalar box functions can be interpreted as volumes of
geodesic tetrahedra embedded in a copy of AdS_5 that has dual conformal
space-time as boundary. When the tetrahedron is space-like, it lies in a
totally geodesic hyperbolic three-space inside AdS_5, with its four vertices on
the boundary. It is a classical result that the volume of such a tetrahedron is
given by the Bloch-Wigner dilogarithm and this agrees with the standard physics
formulae for such box functions. The combinations of box functions that arise
in the n-particle one-loop MHV amplitude in N=4 super Yang-Mills correspond to
the volume of a three-dimensional polytope without boundary, all of whose
vertices are attached to a null polygon (which in other formulations is
interpreted as a Wilson loop) at infinity.Comment: 16 pages, 5 figure
Basics of Generalized Unitarity
We review generalized unitarity as a means for obtaining loop amplitudes from
on-shell tree amplitudes. The method is generally applicable to both
supersymmetric and non-supersymmetric amplitudes, including non-planar
contributions. Here we focus mainly on N=4 Yang-Mills theory, in the context of
on-shell superspaces. Given the need for regularization at loop level, we also
review a six-dimensional helicity-based superspace formalism and its
application to dimensional and massive regularizations. An important feature of
the unitarity method is that it offers a means for carrying over any identified
tree-level property of on-shell amplitudes to loop level, though sometimes in a
modified form. We illustrate this with examples of dual conformal symmetry and
a recently discovered duality between color and kinematics.Comment: 37 pages, 10 figures. Invited review for a special issue of Journal
of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R.
Roiban(ed), M. Spradlin(ed), A. Volovich(ed
Y-system for Scattering Amplitudes
We compute N=4 Super Yang Mills planar amplitudes at strong coupling by
considering minimal surfaces in AdS_5 space. The surfaces end on a null
polygonal contour at the boundary of AdS. We show how to compute the area of
the surfaces as a function of the conformal cross ratios characterizing the
polygon at the boundary. We reduce the problem to a simple set of functional
equations for the cross ratios as functions of the spectral parameter. These
equations have the form of Thermodynamic Bethe Ansatz equations. The area is
the free energy of the TBA system. We consider any number of gluons and in any
kinematic configuration.Comment: 69 pages, 19 figures, v2: references added, minor addition
D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring
Invariance of the AdS_4 x CP^3 superstring under D=3 N=6 superconformal
symmetry is discussed in the sector described by the OSp(4|6)/(SO(1,3) x U(3))
supercoset sigma-model action presented in the conformal basis for the
osp(4|6)/(so(1,3) x u(3)) Cartan forms. Transformation rules under D=3 N=6
superconformal symmetry for the (10|24)-dimensional 'reduced' AdS_4 x CP^3
superspace coordinates are obtained and used to derive corresponding
world-sheet currents.Comment: LaTeX, 23 pages; v2: presentation refined, typos corrected,
references adde