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Abstract

In this paper we apply the Sen formalism, which is originally developed for chiral form fields, to construct non-linear $SL(2,\mathbb{R})$ duality-symmetric actions in four dimensions. The non-linear actions contain a potential term whose allowed form satisfies a condition arising from a requirement that twisted self-duality condition of the theory is equivalent to a constitutive relation. This condition can be perturbatively solved to obtain the potential term. In special cases such as DBI theory or D3-brane, the potential term has a closed form. In particular, we construct the $SL(2,\mathbb{R})$ duality-symmetric D3-brane action coupled to the type IIB supergravity background in the Sen formalism Key features of the Sen formalism are also present in the duality-symmetric actions. For example, there are unphysical fields with the wrong sign of kinetic terms. These fields are uncoupled from physical fields at the equations of motion level. We show that the constructed duality-symmetric D3-brane action also has symmetries such as diffeomorphism and kappa symmetry. The action also gives required equations of motion. Hamiltonian analysis is also studied. The decoupling between physical and unphysical sectors are also shown at the Hamiltonian level.