Self-duality of Born-Infeld action and Dirichlet 3-brane of type IIB superstring theory

TL;DR

This paper demonstrates that the 3-brane action in type IIB superstring theory exhibits SL(2,Z) self-duality, highlighting its special role and suggesting a potential 12-dimensional reformulation of the theory.

Contribution

It establishes the self-duality of the 3-brane Born-Infeld action under SL(2,Z) transformations, linking brane dynamics with fundamental symmetries of type IIB string theory.

Findings

3-brane action is SL(2,Z) self-dual

Indicates a special role for 3-branes in type IIB theory

Suggests a possible 12-dimensional reformulation

Abstract

D-brane actions depend on a world-volume abelian vector field and are described by Born-Infeld-type actions. We consider the vector field duality transformations of these actions. Like the usual 2d scalar duality rotations of isometric string coordinates imply target space T-duality, this vector duality is intimately connected with SL(2,Z)-symmetry of type IIB superstring theory. We find that in parallel with generalised 4-dimensional Born-Infeld action, the action of 3-brane of type IIB theory is SL(2,Z) self-dual. This indicates that 3-brane should play a special role in type IIB theory and also suggests a possibility of its 12-dimensional reformulation.