Super Yang-Mills Operators from the D3-brane Action in a Curved Background

A consistent truncation of IIB on S^5 has been obtained in the sector of the metric and the 4-form potential. The ansatz contains 20 scalars and all 15 gauge fields of $\mathcal{N}=8$ gauged supergravity in five dimensions. With this fully non-linear ansatz, the calculations for n-point correlators of super Yang-Mills (SYM) theory via AdS/CFT are simpler than those in the literature that use {\em linear} ansatz followed by non-linear field redefinitions. We work out the SYM operators that couple to the scalars by expanding the Dirac-Born-Infeld (DBI) action plus Wess-Zumino (WZ) terms around an $Ad{S}_5{\text{timesS}}^5$ background with the metric fluctuations. The resulting operators agree with those based on a superconformal symmetry argument. We discuss the significance of our results.