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TITLE: Actions for (twisted) self-duality equations, their abelian interacting generalizations and applications

ABSTRACT: I will summarise the ongoing research program, where we derive Lorentz invariant Lagrangians for first order equations describing p-form dynamics, and apply them for several well-known problems. First, we derive the most general non-linear electrodynamics theory in 3+1 dimensions in a democratic formulation, where electric and magnetic potentials enter on equal footing. This includes infinitely many duality-symmetric theories where both S-duality and Lorentz invariance are manifest symmetries of the action. Next, we derive non-linear self-interactions of self-dual (chiral) p-forms in Minkowski spaces of d=4k+2 dimensions, for which the Lorentz-covariant formulation is usually challenging even for the free action. We then generalize these results to a democratic description of arbitrary abelian interacting p-forms in arbitrary dimensions. We also apply our formulation to derive actions for type II supergravities in 9+1 dimensions employing a democratic description of all RR fields. For type IIB, the self-duality equation for the five form is a consequence of the Euler-Lagrange equations, as opposed to pseudo-action formulations. Time permitting, I will compare our formulation to other existing ones as well as mention an ongoing work relating these results to another formulation via topological field theory