Abelian and Non-abelian D-brane Effective Actions

TL;DR

This thesis develops a method to derive D-brane effective actions using BPS equations, successfully calculating higher-order corrections in both abelian and non-abelian cases, and explores superspace construction for further analysis.

Contribution

It introduces a novel approach based on BPS equations to systematically derive D-brane effective actions, including all-order corrections in the abelian case and up to order α'^4 in the non-abelian case.

Findings

Calculated all-order four-derivative corrections in the abelian case.

Obtained the effective action up to order α'^4 in the non-abelian case.

Discussed spectrum checks via strings between intersecting branes.

Abstract

In this Ph.D. thesis we review and elaborate on a method to find the D-brane effective action, based on BPS equations. Firstly, both for the Yang-Mills action and the Born-Infeld action it is shown that these configurations are indeed BPS, i.e. solutions to these equations saturate a Bogomolny bound and leave some supersymmetry unbroken. Next, we use the BPS equations as a tool to construct the D-brane effective action and require that (a deformation of) these equations should still imply the equations of motion in more general cases. In the abelian case we managed to calculate all order in $\alpha'$ four-derivative corrections to the effective action and the BPS equations while in the non-abelian case we obtained the effective action up to order $\alpha'^4$. Furthermore, we discuss a check based on the spectrum of strings stretching between intersecting branes. Finally, this Ph.D. thesis also discusses the construction of a boundary superspace which is the first step to use the method of Weyl invariance in N=2 superspace in order to again construct the D-brane effective action. A more detailed summary of each chapter can be found in the introduction.