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

We propose a complete Born–Infeld–like action for a bosonic 5–brane with a worldvolume chiral field in a background of gravitational and antisymmetric gauge fields ofD = 11 supergravity. When the five–brane couples to a three–rank antisymmetric gauge field, local 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. PACS numbers: 11.15-q, 11.17+y