Abstract
We establish self-duality of super D3-brane theory as an exact symmetry of the action both in the Lagrangian and Hamiltonian formalisms. In the Lagrangian formalism, the action is shown to satisfy the Gaillard-Zumino condition. This algebraic relation is recognized in our previous paper to be a necessary and sufficient condition for generic action of U(1) gauge field strength coupled with gravity and matters to be self-dual. For the super D3-brane action, SO(22) duality transformation of a world-volume gauge field should be associated with SO(2) rotation of fermionic brane coordinates in the N = 2 SUSY multiplet. This SO(2) duality symmetry is lifted to SL(2, R ) symmetry in the presence of a dilaton and axion background fields. In the canonical formalism, we show that the duality rotation is described by a canonical transformation, and the Hamiltonian of the D3-brane action is invariant under the transformation.
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