On super form factors of half-BPS operators in \( \mathcal{N} \) =4 super Yang-Mills

We compute form factors of half-BPS operators in \( \mathcal{N} \) = 4 super Yang-Mills dual to massive Kaluza-Klein modes in supergravity. These are appropriate supersymmetrisations \( {{\mathcal{T}}_k} \) of the scalar operators Tr (ϕ k ) for any k, which for k = 2 give the chiral part of the stress-tensor multiplet operator. Using harmonic superspace, we derive simple Ward identities for these form factors, which we then compute perturbatively at tree level and one loop. We propose a novel on-shell recursion relation which links form factors with different numbers of fields. Using this, we conjecture a general formula for the n-point MHV form factors of \( {{\mathcal{T}}_k} \) for arbitrary k and n. Finally, we use supersymmetric generalised unitarity to derive compact expressions for all one-loop MHV form factors of \( {{\mathcal{T}}_k} \) in terms of one-loop triangles and finite two-mass easy box functions.