Born-Infeld Corrections to D3 brane Action in $AdS_5\times S_5$ and N=4, d=4 Primary Superfields

TL;DR

This work analyzes supersymmetric Born-Infeld corrections to the D3-brane action in $AdS_5\times S^5$ and demonstrates that these non-linear couplings reproduce the KK spectrum of Type IIB supergravity as components of N=4 primary superfields $A_p=\mathrm{Tr}W^p$. By decomposing to $N=1$ supersymmetry, the authors identify s-wave singlet operators $O_2$, $O_3$, and $O_4$ (constructed from $F_{\\mu\nu}$ and its dual) multiplied by $Y_p(\hat{\phi})$, and show that the dimensions $E_0$ and masses satisfy the AdS/CFT relations $m^2=E_0(E_0-4)$ for scalars and $m^2=(E_0-2)^2$ for tensors, in agreement with the KK spectrum. Expanding the BI action around the $AdS_5\times S^5$ background and turning on background supergravity fields yields leading couplings to these singlet modes, including Wess-Zumino terms and a supersymmetric completion, thereby linking non-linear D3-brane dynamics to boundary conformal operators. The results reinforce the AdS/CFT dictionary for the graviton multiplet and its KK excitations and suggest avenues to extend the analysis to the full KK tower and non-abelian generalizations, with potential cross-checks via absorption/reaction approaches.

Abstract

We consider certain supersymmetric Born-Infeld couplings to the D3 brane action and show that they give rise to massless and massive KK excitations of type IIB on $AdS_5\times S_5$, in terms of singleton Yang-Mills superfields.