We study double soft theorem for the generalised biadjoint scalar field theory whose amplitudes are computed in terms of punctures on \mathbb{CP}^{k-1}ℂℙk−1. We find that whenever the double soft limit does not decouple into a product of single soft factors, the leading contributions to the double soft theorems come from the degenerate solutions, otherwise the non-degenerate solutions dominate. Our analysis uses the regular solutions to the scattering equations. Most of the results are presented for k=3k=3 but we show how they generalise to arbitrary kk. We have explicit analytic results, for any kk, in the case when soft external states are adjacent.

Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured ℂℙk − 1, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and $$ {\mathcal{D}}_n $$ D n cluster polytope have been established. In this paper using the Gr (3, 6) cluster algebra, we relate the singularities of (3, 6) amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the $$ {\mathcal{D}}_4 $$ D 4 cluster polytope. We also study factorisation properties of the (3, 6) amplitude at various boundaries in the worldsheet.

We use massive spinor helicity formalism to study scattering amplitudes in \mathcal{N}=2^*𝒩=2* super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute amplitudes using projection from \mathcal{N}=4𝒩=4 theory and write three point amplitudes in a convenient form using special kinematics. We then compute four point amplitudes by carrying out massive BCFW shift of the amplitudes. We find some of the shifted amplitudes have a pole at z=\inftyz=∞. Taking the residue at z=\inftyz=∞ into account ensures little group covariance of the final result.