Lagrangian formulations of self-dual gauge theories in diverse dimensions

In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral n-form gauge theories, for n=2p in D=4p+2 dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG model, we generalize the earlier Lagrangian formulation based on a decomposition of spacetime into (D−1) dimensions plus a special dimension, to construct Lagrangian formulations based on a generic decomposition of spacetime into D′ and D″=D−D′ dimensions. Although the Lorentz symmetry is not manifest, we prove that the action is invariant under modified Lorentz transformations.