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We construct the low energy effective action for the bosonic sector on a Dp-brane in large constant RR (p-1)-form field background. The action is invariant under both U(1) gauge symmetry and the volume-preserving diffeomorphism characterizing the RR-field background. Scalar fields representing transverse coordinates of the Dp-brane are included. It also respects T-duality and is consistent with the action for M5-brane in C-field background.

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