Different formulations of chiral bosons

It is shown, that recently constructed PST Lagrangians for chiral supergravities follow directly from earlier Kavalov-Mkrtchyan Lagrangians by an Ansatz for the θ tensor by expressing this in terms of the PST scalar. The susy algebra which included earlier α-symmetry in the commutator of supersymmetry transformations, is now shown to include both PST symmetries, which arise from the single α-symmetry term. The Lagrangian for the 5-brane is not described by this correspondence, and probably can be obtained from more general Lagrangians, possessing α-symmetry.