Higher derivative couplings of hypermultiplets

We construct the four-derivative supersymmetric extension of (1, 0), 6D supergravity coupled to Yang-Mills and hypermultiplets. The hypermultiplet scalars are taken to parametrize the quaternionic projective space Hp(n) = Sp(n, 1)/Sp(n) x Sp(1)(R). The hyperscalar kinetic term is not deformed, and the quaternionic Kahler structure and symmetries of Hp(n) are preserved. The result is a three parameter Lagrangian supersymmetric up to first order in these parameters. Considering the case of Hp(1) we compare our result with that obtained from the compactification of 10D heterotic supergravity on four-torus, consistently truncated to N = (1, 0), in which the hyperscalars parametrize SO(1, 4)/SO(4). We find that depending on how the Sp(1) is embedded in the SO(4), the results agree for a specific value of the parameter that governs the higher derivative hypermultiplet couplings.