Abstract: The infra-red limit of a planar static D3-brane in AdS is a tensionless D3-brane at the anti-de Sitter horizon with dynamics governed by a strong-field limit of the Dirac–Born–Infeld action, analogous to that found from the Born–Infeld action by Bialynicki-Birula. As in that case, the field equations are those of an interacting 4D conformal invariant field theory with an electromagnetic duality invariance, but the D3-brane origin makes these properties manifest. We also find an -invariant action for these equations.