Contents

# Contents

## Idea

The Green-Schwarz action functional for super D-branes contains a generalization of the Nambu-Goto action in which the volume form is modified by the field strength of the Chan-Paton gauge field on the worldvolume of the D-brane. This modified Nambu-Goto action is referred to as the Dirac-Born-Infeld action or DBI action, for short.

## References

### General

Named after Paul Dirac, Max Born and Leopold Infeld.

Review:

• Paul Koerber, Abelian and Non-abelian D-brane Effective Actions, Fortsch. Phys. 52 (2004) 871-960 (arXiv:hep-th/0405227)

Detailed discussion of the relation to the Polyakov action and the Nambu-Goto action is in

### For single D-branes

In the low energy action functional for single D-branes the DBI action is due to

and a full $\kappa$-symmetric Green-Schwarz sigma-model for D-branes:

Review:

Discussion in terms of D-branes as leaves of Dirac structures on Courant Lie 2-algebroids of type II geometry is in

• Tsuguhiko Asakawa, Shuhei Sasa, Satoshi Watamura, D-branes in Generalized Geometry and Dirac-Born-Infeld Action (arXiv:1206.6964)

• Martin Cederwall, Alexander von Gussich, Aleksandar Mikovic, Bengt Nilsson, Anders Westerberg, On the Dirac-Born-Infeld Action for D-branes, Phys.Lett.B390:148-152, 1997 (arXiv:hep-th/9606173)

• Ian I. Kogan, Dimitri Polyakov, DBI Action from Closed Strings and D-brane second Quantization, Int. J. Mod. Phys. A18 (2003) 1827 (arXiv:hep-th/0208036)

### For coincident (non-abelian) D-branes

Discussion of the generalization of the DBI action to non-abelian Chan-Paton gauge fields (hence: for coincident D-branes) includes the following:

A proposal for the formulation by using the symmetrized trace is due to

followed by

Review includes:

• W. Chemissany, On the way of finding the non-Abelian Born-Infeld theory, 2004 (spire:1286212 pdf)

Issues with this proposal at higher order have been found in

Correction terms have been proposed in

and a completely different approach via TT deformation of the abelian DBI action is proposed in

• T. Daniel Brennan, Christian Ferko, Savdeep Sethi, A Non-Abelian Analogue of DBI from $T \bar T$ (arXiv:1912.12389)

For actual derivation of gauge enhancement on coincident D-branes see the references there.

### Single trace observables as weight systems on chord duagrams

Relation of single trace observables in the non-abelian DBI action on Dp-D(p+2)-brane bound states (hence Yang-Mills monopoles) to su(2)-Lie algebra weight systems on chord diagrams computing radii averages of fuzzy spheres:

Last revised on January 12, 2020 at 16:27:47. See the history of this page for a list of all contributions to it.