Within the framework of six-dimensional N = ( 1 , 0 ) conformal supergravity, we introduce new off-shell multiplets O ? ( n ) , where n = 3 , 4 , … , and use them to construct higher-rank extensions of the linear multiplet action. The O ? ( n ) multiplets may be viewed as being dual to well-known superconformal O ( n ) multiplets. We provide prepotential formulations for the O ( n ) and O ? ( n ) multiplets coupled to conformal supergravity. For every O ? ( n ) multiplet, we construct a higher derivative invariant which is superconformal on arbitrary superconformally flat backgrounds. We also show how our results can be used to construct new higher derivative actions in supergravity.
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