Search for Duality Symmetries in p-Brane Theories

TL;DR

This paper investigates the presence of $SL(2)$ duality symmetries in p-brane theories, revealing conditions under which full or partial duality groups are realized, with implications for worldvolume dynamics and constraints.

Contribution

It demonstrates that an $SL(2)$ duality symmetry can be realized in p-brane theories, with full symmetry in specific dimensional cases and partial symmetry generally, linking duality to worldvolume constraints.

Findings

Full $SL(2)$ symmetry in p-branes in p+1 dimensions.

Partial $SL(2)$ symmetry for general p-branes.

Duality transformations preserve worldvolume constraints.

Abstract

The requirement of an $SL(2)$ duality symmetry, mixing the worldvolume field equations with Bianchi identities, leads to a highly nonlinear equation involving the transformation parameters and certain worldvolume currents. In general, this equation seems to admit a solution only for a two parameter subgroup of the seeked $SL(2)$. These transformations also leave invariant the first class constraints generating the worldvolume reparametrizations. In the special case of $p$--branes in $p+1$ dimensions, the full $SL(2)$ is realized.