We construct the Dirac-Born-Infeld action in the context of $\mathcal{N}=1$ conformal supergravity and its possible extensions including matter couplings. We especially focus on the Volkov-Akulov constraint, which is important to avoid ghost modes from the higher derivative terms. In the case with matter couplings, we find the modified D-term potential.

• Received 14 April 2015

DOI:https://doi.org/10.1103/PhysRevD.92.025017