Fermionic extension of the scalar Born–Infeld equation and its relation to the supersymmetric Chaplygin gas

In this Letter, we present a fermionic extension of the scalar Born–Infeld equation, which has been derived from the Nambu–Goto superstring action in (2+1)(2+1) dimensions through the Cartesian parameterization. It is demonstrated that in the relativistic limit where c→∞c→∞, the fermionic Born–Infeld model reduces to the supersymmetric Chaplygin gas model in one spatial dimension. However, the supersymmetry itself is not preserved.