Massive amplitudes on the Coulomb branch of N=4 SYM

Abstract

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.

29 pages, 1 figure

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• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• The Coulomb-branch S-matrix from massless amplitudes
• The two-loop six-point amplitude in ABJM theory
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Massive On-shell Recursion Relations for n-point Amplitudes
• Open associahedra and scattering forms
• The dimension-shift conjecture for one-loop amplitudes
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• Multigluon tree amplitudes with a pair of massive fermions
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Holonomies of gauge fields in twistor space 5: amplitudes of gluons and massive scalars
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions
• General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion
• Instanton corrections to the effective action of N=4 SYM
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• Yangian-Like Symmetry of Probe-Brane Actions
• String Theory from Maximal Supersymmetry
• A note on scattering amplitudes on the moduli space of ABJM
• Towards Amplituhedron via One-Dimensional Theory
• A new approach for amplitudes with multiple fermion lines