Higher derivative couplings of hypermultiplets

Abstract

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 $Hp(n)=Sp(n,1)/Sp(n)\times Sp(1{)}_R$. The hyperscalar kinetic term is not deformed, and the quaternionic Kähler 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 $SO(4,1)/SO(4)$. We find that depending on how $Sp(1)\subset Sp(1,1)$ is embedded in $SO(4)$, the results agree for a specific value of the parameter that governs the higher derivative hypermultiplet couplings.

arXiv comment29 pages

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