272 research outputs found
Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
We show that three-dimensional supergravity amplitudes can be obtained as
double copies of either three-algebra super-Chern-Simons matter theory or that
of two-algebra super-Yang-Mills theory, when either theory is organized to
display the color-kinematics duality. We prove that only helicity-conserving
four-dimensional gravity amplitudes have nonvanishing descendants when reduced
to three dimensions; implying the vanishing of odd-multiplicity S-matrix
elements, in agreement with Chern-Simons matter theory. We explicitly verify
the double-copy correspondence at four and six points for N=12,10,8
supergravity theories and discuss its validity for all multiplicity.Comment: 5 pages, published version in PR
ABJM amplitudes and the positive orthogonal grassmannian
A remarkable connection between perturbative scattering amplitudes of
four-dimensional planar SYM, and the stratification of the positive
grassmannian, was revealed in the seminal work of Arkani-Hamed et. al. Similar
extension for three-dimensional ABJM theory was proposed. Here we establish a
direct connection between planar scattering amplitudes of ABJM theory, and
singularities there of, to the stratification of the positive orthogonal
grassmannian. In particular, scattering processes are constructed through
on-shell diagrams, which are simply iterative gluing of the fundamental
four-point amplitude. Each diagram is then equivalent to the merging of
fundamental OG_2 orthogonal grassmannian to form a larger OG_k, where 2k is the
number of external particles. The invariant information that is encoded in each
diagram is precisely this stratification. This information can be easily read
off via permutation paths of the on-shell diagram, which also can be used to
derive a canonical representation of OG_k that manifests the vanishing of
consecutive minors as the singularity of all on-shell diagrams. Quite
remarkably, for the BCFW recursion representation of the tree-level amplitudes,
the on-shell diagram manifests the presence of all physical factorization
poles, as well as the cancellation of the spurious poles. After analytically
continuing the orthogonal grassmannian to split signature, we reveal that each
on-shell diagram in fact resides in the positive cell of the orthogonal
grassmannian, where all minors are positive. In this language, the amplitudes
of ABJM theory is simply an integral of a product of dlog forms, over the
positive orthogonal grassmannian.Comment: 52 pages: v2, typos corrected, published version in JHE
A new integral formula for supersymmetric scattering amplitudes in three dimensions
We propose a new integral formula for all tree-level scattering amplitudes of
N=6 supersymmetric Chern-Simons theory. It resembles the
Roiban-Spradlin-Volovich-Witten formula for N=4 supersymmetric Yang-Mills
theory based on a twistor string theory formulation. Our formula implies that
the (2k)-point tree-level amplitude is closely related to degree (k-1) curves
in CP^{k-1}.Comment: 4 pages; v2. references adde
S-matrix singularities and CFT correlation functions
In this note, we explore the correspondence between four-dimensional flat
space S-matrix and two-dimensional CFT proposed by Pasterski et al. We
demonstrate that the factorization singularities of an n-point cubic diagram
reproduces the AdS Witten diagrams if mass conservation is imposed at each
vertex. Such configuration arises naturally if we consider the 4-dimensional
S-matrix as a compactified massless 5-dimensional theory. This identification
allows us to rewrite the massless S-matrix in the CHY formulation, where the
factorization singularities are re-interpreted as factorization limits of a
Riemann sphere. In this light, the map is recast into a form of 2d/2d
correspondence.Comment: 18 page
Scattering Amplitudes For All Masses and Spins
We introduce a formalism for describing four-dimensional scattering
amplitudes for particles of any mass and spin. This naturally extends the
familiar spinor-helicity formalism for massless particles to one where these
variables carry an extra SU(2) little group index for massive particles, with
the amplitudes for spin S particles transforming as symmetric rank 2S tensors.
We systematically characterise all possible three particle amplitudes
compatible with Poincare symmetry. Unitarity, in the form of consistent
factorization, imposes algebraic conditions that can be used to construct all
possible four-particle tree amplitudes. This also gives us a convenient basis
in which to expand all possible four-particle amplitudes in terms of what can
be called "spinning polynomials". Many general results of quantum field theory
follow the analysis of four-particle scattering, ranging from the set of all
possible consistent theories for massless particles, to spin-statistics, and
the Weinberg-Witten theorem. We also find a transparent understanding for why
massive particles of sufficiently high spin can not be "elementary". The Higgs
and Super-Higgs mechanisms are naturally discovered as an infrared unification
of many disparate helicity amplitudes into a smaller number of massive
amplitudes, with a simple understanding for why this can't be extended to
Higgsing for gravitons. We illustrate a number of applications of the formalism
at one-loop, giving few-line computations of the electron (g-2) as well as the
beta function and rational terms in QCD. "Off-shell" observables like
correlation functions and form-factors can be thought of as scattering
amplitudes with external "probe" particles of general mass and spin, so all
these objects--amplitudes, form factors and correlators, can be studied from a
common on-shell perspective.Comment: 79 page
Worldgraph Approach to Yang-Mills Amplitudes from N=2 Spinning Particle
By coupling the N=2 spinning particle to background vector fields, we
construct Yang-Mills amplitudes for trees and one loop. The vertex operators
are derived through coupling the BRST charge; therefore background gauge
invariance is manifest, and the Yang-Mills ghosts are automatically included in
loop calculations by worldline ghosts. Inspired by string calculations, we
extend the usual worldline approach to incorporate more "generalized" 1D
manifolds. This new approach should be useful for constructing higher-point and
higher-loop amplitudes.Comment: 21 pages, 4 figures; v2: 22 pages, 5 figures, major changes in
section V, typos correcte
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