Self-duality in Super D3-brane Action

TL;DR

This paper proves that the super D3-brane action exhibits exact self-duality symmetry in both Lagrangian and Hamiltonian formalisms, involving U(1) gauge fields, fermionic coordinates, and background scalar fields, with implications for string theory dualities.

Contribution

It demonstrates the self-duality of super D3-brane theory as an exact symmetry, extending previous conditions to include fermionic and background field effects.

Findings

Super D3-brane action satisfies Gaillard-Zumino condition.

Duality transformation corresponds to a canonical transformation.

Hamiltonian remains invariant under duality rotation.

Abstract

We establish self-duality of super D3-brane theory as an exact symmetry of the action both in the Lagrangian and Hamiltonian formalism. 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(2) duality transformation of a world-volume gauge field should be associated with SO(2) rotation of fermionic brane coordinates in N=2 SUSY multiplet. This SO(2) duality symmetry is lifted to SL(2,R) symmetry in the presence of a dilaton and an 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.