The Moduli Spaces of Worldvolume Brane Solitons

TL;DR

This paper calculates the geometric structure of moduli spaces for various worldvolume brane solitons, revealing hyper-K"ahler and octonionic K"ahler geometries with torsion, advancing understanding of brane dynamics.

Contribution

It provides explicit computations of the moduli space metrics for D-brane and M-5-brane solitons, identifying their complex geometric structures with torsion.

Findings

Moduli space of D-4-brane 0-brane solitons is hyper-K"ahler with torsion.

Moduli space of D-8-brane 0-brane solitons is octonionic K"ahler with torsion.

Moduli space of M-5-brane self-dual string is hyper-K"ahler with torsion.

Abstract

We compute the moduli metrics of worldvolume 0-brane solitons of D-branes and the worldvolume self-dual string solitons of the M-5-brane and examine their geometry. We find that the moduli spaces of 0-brane solitons of D-4-branes and D-8-branes are hyper-K\"ahler manifolds with torsion and octonionic K\"ahler manifolds with torsion, respectively. The moduli space of the self-dual string soliton of the M-5-brane is also a hyper-K\"ahler manifold with torsion.