Brane actions with chiral bosons present special challenges. Recent progress in the description of the two main examples -the M theory five-brane and the heterotic string -is described. Also, double dimensional reduction of the M theory five-brane on K3 is shown to give the heterotic string.
The Bosonic Part of the Five-Brane ActionThe M theory five-brane action contains a tensor gauge field, which (in linearized approximation) has a self-dual field strength. Ref.[1] analyzed the problem of coupling a 6d self-dual tensor gauge field to a metric field so as to achieve general coordinate invariance.It presented a formulation in which one direction is treated differently from the other five.At the time that work was done, the author knew of no straightforward way to make the general covariance manifest. However, shortly thereafter a paper appeared [2] that presents equivalent results using a manifestly covariant formulation [3], which we refer to as the PST formulation. In the following both approaches and their relationship are described. These results have been generalized to supersymmetric actions with local kappa symmetry [4,5,6], but here we will only consider the bosonic theories.
The Noncovariant FormulationLet us denote the 6d (world volume) coordinates by σμ = (σ µ , σ 5 ), where µ = 0, 1, 2, 3, 4.The σ 5 direction is singled out as the one that will be treated differently from the other 1 Talk presented at the Trieste Conference on Duality Symmetries in String Theory -II