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We construct the Dirac-Born-Infeld action in the context of N=1 conformalsupergravity and its possible extensions including matter couplings. Weespecially focus on the Volkov-Akulov constraint, which is important to avoidghost modes from the higher derivative terms. In the case with mattercouplings, we find the modified D-term potential.

Matter coupled Dirac-Born-Infeld action in 4-dimensional N=1 conformal supergravity