Comments on Three-Branes

TL;DR

This paper derives the effective world-volume theory of a 3-brane from a supersymmetric D-brane description, showing its invariance under certain duality transformations and connecting it to four-dimensional gauge theories.

Contribution

It presents a manifestly supersymmetric derivation of the 3-brane's effective theory and explores its duality invariance and relation to 4D gauge solitons.

Findings

Effective 3-brane theory is invariant under SL(2,R) transformations.

Two-brane system involves massive supermultiplets transforming under SL(2,Z).

Connection established between brane dynamics and 4D N=4 Yang-Mills solitons.

Abstract

The Born--Infeld-like effective world-volume theory of a single 3-brane is deduced from a manifestly space-time supersymmetric description of the corresponding $D$-brane. This is shown to be invariant under $SL(2,R)$ transformations that act on the abelian gauge field as well as the bulk fields. The effective theory of two nearby parallel three-branes involves massive world-volume supermultiplets which transform under $SL(2,Z)$ into the dyonic solitons of four-dimensional $N=4$ spontaneously broken $SU(2)$ Yang--Mills theory.