Manifestly covariant polynomial M5-brane lagrangians

We present polynomial and manifestly covariant M5-brane Lagrangians along
with their analyses involving their dynamics, gauge symmetries and their nonlinear self-
duality condition. Such Lagrangians can be particularly useful for developments that are
otherwise hindered by a non-polynomial structure and singularity of the Lagrangian such as
its quantisation. Although on integrating out some of the auxiliary fields these polynomial
Lagrangians reduce to the M5-brane Lagrangian given by the Pasti-Sorokin-Tonin (PST)
formalism, in the analysis of the polynomial Lagrangians the only remnant of the non-
polynomial structure of the PST type Lagrangian appears in the gauge transformation
corresponding to an infinitesimal shift of a Stückelberg field. This transformation does
not affect the dynamics or the on-shell self-duality condition of the polynomial M5-brane
Lagrangians.