Abstract
We study scattering amplitudes of massive BPS states on the Coulomb branch of 4d mathcal{N} = 4 super-Yang-Mills, utilising a little group covariant on-shell superspace for massive particles. Super-BCFW recursion for massive amplitudes is constructed and its validity is proven for all Coulomb branch superamplitudes. We then determine the exact three-particle superamplitudes for massive states. These ingredients allow us to explicitly compute the four- and five-particle superamplitudes, which is the first non-trivial usage of BCFW recursion for amplitudes with entirely massive external states. The manifest little group covariance helps clarify both the role of special kinematic properties of BPS states and the organizational structures of the superamplitudes.
Highlights
Dualconformal symmetry [7, 8], Yangian symmetry and integrable structure [9], constructibility of tree [10] amplitudes by BCFW recursion [11, 12], loop integrands by on-shell diagrams and full constructibility from leading singularities [13, 14] and the interpretation of amplitudes as volumes of polytopes [15, 16]
We study scattering amplitudes of massive BPS states on the Coulomb branch of 4d N = 4 super-Yang-Mills, utilising a little group covariant on-shell superspace for massive particles
The spinor helicity formalism has provided a set of variables with respect to which a broad set of phenomena can be formulated and uncovered on-shell purely through recourse to fundamental principles of quantum mechanics and relativity, without introducing quantum fields and path integrals and their associated unphysical redundancies
Summary
In [29] we construct on-shell superspaces for massive supermultiplets that are covariant in the SU(2) little group, recently introduced into helicity spinors in [30]. The case |Zi| = 2mi is the special BPS limit and will be relevant for states on the Coulomb branch For these representations, half of the supercharges are eliminated through the reality constraint qi,I A. For non-BPS representations with a central charge, linear combinations of supercharges may be found that will satisfy the algebra (2.3) with Zi,AB = 0. The explicit SU(N ) automorphism symmetry of the SUSY algebra is broken to USP(N ) by the central charge of these massive single particle states, which is exactly the massive R-symmetry group expected for a theory with half of the number of supersymmetries. Supermultiplets may be represented as coherent states which are eigenstates of N ‘lowering operators’ To build these states we introduce Grassmann variables which transform as fundamental spinors of the little group of each particle ηiA,I , as well as their conjugates ηi†,IA.
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