Geometry of the Nonabelian DBI Dyonic Instanton

TL;DR

This paper develops a calculus for Lie algebra valued functions in the nonabelian DBI action and demonstrates that a dyonic instanton solution exhibits a novel brane 'blowing-up' effect, representing a superposition of D0 and F1 branes.

Contribution

It introduces a calculus for Lie algebra functions in the nonabelian DBI action and shows the dyonic instanton as a full solution with a new geometric 'blowing-up' phenomenon.

Findings

The dyonic instanton solves the full nonabelian DBI equations.

The solution exhibits a 'blowing-up' of the brane not seen in monopole cases.

The instanton represents a superposition of D0 and F1 branes between D4 branes.

Abstract

We introduce a calculus of the Lie algebra valued functions present in Tseytlin's proposal for the nonabelian DBI action, and apply it to show that the recently found dyonic instanton is a solution of the full nonabelian DBI action. The geometry of this solution exhibits a new effect of ``blowing-up'' of the brane, which was not present in the case of the brane realisation of monopoles. We interpret this solution as the superposition of the D0 brane and fundamental string F1 which connects two separated D4 branes. Both F1 and D0 are delocalised in the ``blown-up'' region between two separated D4 branes.