Covariant Action for a D=11 Five-Brane with the Chiral Field

TL;DR

This paper develops a covariant, Born-Infeld-like action for a bosonic 5-brane in eleven-dimensional supergravity, incorporating a chiral field, auxiliary scalar, and Wess-Zumino term, and demonstrates its reduction to a D4-brane action in ten dimensions.

Contribution

It presents a complete covariant action for a D=11 five-brane with a chiral field, including gauge symmetries and a consistent reduction to D=10 branes.

Findings

Constructed a covariant five-brane action with auxiliary scalar.

Included Wess-Zumino term for gauge invariance.

Reduced to D=10 D4-brane Born-Infeld action.

Abstract

We propose a complete Born-Infeld-like action for a bosonic 5-brane with the worldvolume chiral field in a background of gravitational and antisymmetric gauge fields of D=11 supergravity. When the five-brane couples to a three-rank antisymmetric gauge field local worldvolume symmetries of the five-brane require the addition to the action of an appropriate Wess-Zumino term. To preserve general coordinate and Lorentz invariance of the model we introduce a single auxiliary scalar field. The auxiliary field can be eliminated by gauge fixing a corresponding local symmetry at the price of the loss of manifest d=6 worldvolume covariance. The double dimensional reduction of the five-brane model results in the Born-Infeld action with the Wess-Zumino term for a D=10 four-D-brane.