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We present a manifestly supersymmetric description of A and B branes on Kähler manifolds using a completely local N = 2 superspace formulation of the world‐sheet nonlinear σ‐model in the presence of a boundary. In particular, we show that an N = 2 superspace description of type A boundaries is possible. This leads to a concrete realization of the still poorly understood coisotropic A branes. We also discuss briefly how the superspace description of a B brane provides an efficient way to compute higher loop β‐functions. In particular, we sketch how one obtains the fourth order derivative correction to the Born‐Infeld action by using a β‐function method.

A and B branes from N = 2 superspace