Chiral squaring and KLT relations

We demonstrate that amplitudes based on matter supermultiplets can be combined to provide amplitudes of vector supermultiplets by means of KLT relations. In practice we do this by developing a procedure for removing supersymmetry supercharges from super Yang-Mills theory and supergravity supermultiplets, reducing them to vector and chiral supermultiplets respectively. This way, we reduce the super KLT relations to chiral KLT relations making chiral squaring of amplitudes manifest. We study these chiral KLT relations, discussing permutation symmetry and vanishing relations. Finally some explicit calculations are done to show how the relations work in detail.