World-volume fields, SL(2;Z) and duality: The type IIB 3-brane

TL;DR

This paper introduces a method for constructing super-brane actions that naturally incorporate background fields and SL(2;Z) symmetry, demonstrated through the type IIB 3-brane with a self-dual polynomial action.

Contribution

It presents a novel approach to super-brane actions linking background tensor potentials to world-volume fields, ensuring SL(2;Z) symmetry and self-duality in the type IIB 3-brane.

Findings

Constructed a super-brane action with background coupling

Demonstrated SL(2;Z) symmetry in the action

Proved kappa-symmetry invariance requires self-duality

Abstract

We propose a method for constructing super-brane actions where every background tensor potential corresponds to a world-volume field strength. The procedure provides a natural coupling to the background and automatically displays the SL(2;Z) symmetry of the IIB string theory. The Dirichlet 3-brane is used as a test ground for these ideas. A polynomial action consistent with non-linear self-duality is presented. Invariance of the action under kappa-symmetry is demonstrated for arbitrary on-shell type IIB supergravity backgrounds and is shown to require self-duality.