Yang-Mills Instantons Sitting on a Ricci-flat Worldspace of Double D4-brane

TL;DR

This paper constructs SU(2) Yang-Mills instanton solutions on Ricci-flat D4-brane backgrounds within type IIA supergravity, demonstrating their stability and supporting Tseytlin's non-abelian DBI action proposal.

Contribution

It explicitly constructs YM instantons on Ricci-flat D4-brane backgrounds and shows their role in stabilizing probe branes, validating Tseytlin's non-abelian DBI action.

Findings

YM instantons minimize energy on Ricci-flat backgrounds

Stable brane configurations support Tseytlin's non-abelian DBI proposal

Explicit solutions on Taub-NUT and Eguchi-Hanson geometries

Abstract

Thus far, there seem to be no complete criteria that can settle the issue as to what the correct generalization of the Dirac-Born-Infeld (DBI) action, describing the low-energy dynamics of the D-branes, to the non-abelian case would be. According to recent suggestions, one might pass the issue of worldvolume solitons from abelian to non-abelian setting by considering the stack of multiple, coincident D-branes and use it as a guideline to construct or censor the relevant non-abelian version of the DBI action. In this spirit, here we are interested in the explicit construction of SU(2) Yang-Mills (YM) instanton solutions in the background geometry of two coincident probe D4-brane worldspaces particularly when the metric of target spacetime in which the probe branes are embedded is given by the Ricci-flat, magnetic extremal 4-brane solution in type IIA supergravity theory with its worldspace metric being given by that of Taub-NUT and Eguchi-Hanson solutions, the two best-known gravitational instantons. And then we demonstrate that with this YM instanton- gravitational instanton configuration on the probe D4-brane worldvolume, the energy of the probe branes attains its minimum value and hence enjoys stable state provided one employs the Tseytlin's non-abelian DBI action for the description of multiple probe D-branes. In this way, we support the arguments in the literature in favor of Tseytlin's proposal for the non-abelian DBI action.