nLab
Dirac-Born-Infeld action

Contents

Context

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

String theory

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 κ\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)

See also

  • 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

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.