46 research outputs found
The Two-Loop Symbol of all Multi-Regge Regions
We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam
regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the
number of distinct Mandelstam regions grows exponentially with n, the increase
of independent symbols turns out to be merely quadratic. We uncover how to
construct the symbols for any number of external gluons from just two building
blocks which are naturally associated with the six- and seven-gluon amplitude,
respectively. The second building block is entirely new, and in addition to its
symbol, we also construct a prototype function that correctly reproduces all
terms of maximal functional transcendentality.Comment: 20 pages, v2: include details on functions f and g, make appendix
consistent with main text, typesetting (published version
Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in
N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman
diagram calculations, solutions to these constraints, namely the four- and
six-point superamplitudes, are presented and shown to be invariant under
Yangian symmetry. This introduces integrability into the amplitude sector of
the theory.Comment: 50 pages. v2, v3: References added, minor correction
New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
We provide evidence for a duality between color and kinematics in
three-dimensional supersymmetric Chern-Simons matter theories. We show that the
six-point amplitude in the maximally supersymmetric, N=8, theory can be
arranged so that the kinematic factors satisfy the fundamental identity of
three-algebras. We further show that the four- and six-point N=8 amplitudes can
be "squared" into the amplitudes of N=16 three-dimensional supergravity, thus
providing evidence for a hidden three-algebra structure in the dynamics of the
supergravity.Comment: 8 pages, 2 figure
Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
We study Yangian-invariant deformations of scattering amplitudes in 4d N=4
supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena
(ABJM) theory. In particular, we obtain the deformed Grassmannian integral for
4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space.
For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We
investigate general deformations of on-shell diagrams, and find the deformed
Grassmannian integral for this theory. We furthermore introduce the algebraic
R-matrix construction of deformed Yangian invariants for ABJM theory.Comment: 39 pages, 9 figures; v2: references added, typos fixed, section 3.4
improved, published versio
Handling Handles: Nonplanar Integrability in Supersymmetric Yang-Mills Theory
We propose an integrability setup for the computation of correlation
functions of gauge-invariant operators in supersymmetric
Yang-Mills theory at higher orders in the large genus expansion
and at any order in the 't Hooft coupling . In
this multi-step proposal, one polygonizes the string worldsheet in all possible
ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over
all hexagon junctions to obtain the full correlator. We test our
integrability-based conjecture against a non-planar four-point correlator of
large half-BPS operators at one and two loops.Comment: 6 pages, 4 figures; v2: updated references, typos, minor improvements
(published version
Higher-Point Integrands in N=4 super Yang-Mills Theory
We compute the integrands of five-, six-, and seven-point correlation
functions of twenty-prime operators with general polarizations at the two-loop
order in N=4 super Yang-Mills theory. In addition, we compute the integrand of
the five-point function at three-loop order. Using the operator product
expansion, we extract the two-loop four-point function of one Konishi operator
and three twenty-prime operators. Two methods were used for computing the
integrands. The first method is based on constructing an ansatz, and then
numerically fitting for the coefficients using the twistor-space reformulation
of N=4 super Yang-Mills theory. The second method is based on the OPE
decomposition. Only very few correlator integrands for more than four points
were known before. Our results can be used to test conjectures, and to make
progresses on the integrability-based hexagonalization approach for correlation
functions.Comment: 50 pages, 2 figures. v2: many changes and additions, files added,
references update
The Multi-Regge Limit from the Wilson Loop OPE
The finite remainder function for planar, color-ordered, maximally helicity
violating scattering processes in N=4 super Yang-Mills theory possesses a
non-vanishing multi-Regge limit that depends on the choice of a Mandelstam
region. We analyze the combined multi-Regge collinear limit in all Mandelstam
regions through an analytic continuation of the Wilson loop OPE. At leading
order, the former is determined by the gluon excitation of the
Gubser-Klebanov-Polyakov string. We illustrate the general procedure at the
example of the heptagon remainder function at two loops. In this case, the
continuation of the leading order terms in the Wilson loop OPE suffices to
determine the two-loop multi-Regge heptagon functions in all Mandelstam regions
from their symbols. The expressions we obtain are fully consistent with recent
results by Del Duca et al.Comment: 35+18 pages, 5 figure
Exacting N=4 Superconformal Symmetry
Tree level scattering amplitudes in N=4 super Yang-Mills theory are almost,
but not exactly invariant under the free action of the N=4 superconformal
algebra. What causes the non-invariance is the holomorphic anomaly at poles
where external particles become collinear. In this paper we propose a
deformation of the free superconformal representation by contributions which
change the number of external legs. This modified classical representation not
only makes tree amplitudes fully invariant, but it also leads to additional
constraints from symmetry alone mediating between hitherto unrelated
amplitudes. Moreover, in a constructive approach it appears to fully constrain
all tree amplitudes when combined with dual superconformal alias Yangian
symmetry.Comment: 47 pages. v2: minor corrections, clarifications and additions;
algebraic derivation of {S,Sbar}=K, v3: section 4.4 restored (it was dropped
by mistake in v2), minor corrections, to appear in JHE