On Different Formulations of Chiral Bosons

TL;DR

This paper demonstrates how recent PST Lagrangians for chiral supergravities derive from earlier Kavalov-Mkrtchyan formulations by an Ansatz involving the $ heta$ tensor, clarifying their relation and symmetries.

Contribution

It reveals the connection between PST and Kavalov-Mkrtchyan Lagrangians for chiral supergravities through an Ansatz, and discusses the role of symmetries in the supersymmetry algebra.

Findings

PST Lagrangians follow from Kavalov-Mkrtchyan Lagrangians via an Ansatz.

The supersymmetry algebra includes both PST symmetries.

The 5-brane Lagrangian likely requires more general formulations with $ extalpha$-symmetry.

Abstract

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