Chiral 2-form actions and their applications to M5-brane(s)

We study the symmetry and dynamics of M5-branes as well as chiral p-forms in this thesis. In the first part, we propose a model describing the gauge sector of multiple M5-branes. The model has modified six-dimensional Lorentz symmetry and its double dimensional reduction gives 5D Yang-Mills theory with higher derivative corrections. The non-abelian self-dual string solutions to this model are presented. In the second part of the thesis, we propose an alternative new action for the single M5-brane. The six-dimentional worldvolume space is covariantly split into 3+3. The relation of the new action to the conventional PST action as well as to the M2- brane action are studied. Finally, we briefly discuss the attempt to formulate the M5-brane action in a 2+4 splitting of worldvolume space and some duality properties and issues of chiral p-form actions.