Considering that the effective theory of closed string tachyons can have world sheet supersymmetry, as shown by Vafa, we study a worldline supersymmetric action in a Friedmann–Robertson–Walker background, for which the superpotential originates a tachyon scalar potential. There are such potentials with spontaneously broken supersymmetry at the instability and supersymmetry after tachyon condensation. Furthermore, given a tachyonic potential, the superpotential can be computed by a power series ansatz and has a free parameter that can be chosen such that complex solutions become real.

• Received 15 November 2013

DOI:https://doi.org/10.1103/PhysRevD.89.043501