On Target-Space Duality in p-Branes

TL;DR

This paper investigates target-space duality in p-branes, revealing how the duality group structure depends on the dimensionality of the spacetime and background fields, with a richer symmetry for lower dimensions.

Contribution

It analyzes the structure of target-space duality transformations in p-branes, identifying the specific duality groups realized in different dimensional settings.

Findings

A $GL(2)$ duality group for $m=0$

A reduced two-parameter duality group for $m>0$

Dependence of duality symmetry on spacetime dimensions

Abstract

We study the target-space duality transformations in $p$--branes as transformations which mix the worldvolume field equations with Bianchi identities. We consider an $(m+p+1)$-dimensional spacetime with $p+1$ dimensions compactified, and a particular form of the background fields. We find that while a $GL(2)=SL(2)\times R$ group is realized when $m=0$, only a two parameter group is realized when $m>0$.