Self-Duality of Super D3-brane Action on $AdS_{5}\times S^{5}$ Background

TL;DR

This paper demonstrates that the super D3-brane action in the $AdS_5 imes S^5$ background is exactly self-dual under electric-magnetic duality and SO(2) rotations, satisfying the Gaillard-Zumino duality condition without gauge fixing.

Contribution

It proves the super D3-brane action's self-duality under duality transformations without gauge fixing, confirming its invariance in the $AdS_5 imes S^5$ background.

Findings

The super D3-brane action is invariant under electric-magnetic duality.

The action satisfies the Gaillard-Zumino duality condition.

Self-duality holds without gauge fixing for $mbda$-symmetry.

Abstract

We show that the super D3-brane action on $AdS_5 \times S^5$ background recently constructed by Metsaev and Tseytlin is exactly invariant under the combination of the electric-magnetic duality transformation of the worldvolume gauge field and the SO(2) rotaion of N=2 spinor coordinates. The action is shown to satisfy the Gaillard-Zumino duality condition, which is a necessary and sufficient condition for a action to be self-dual. Our proof needs no gauge fixing for the $\kappa$-symmetry.