Supersymmetric D3 brane action in AdS_5 x S^5

TL;DR

This work constructs a manifestly space-time supersymmetric and κ-invariant D3-brane action for a probe in $AdS_5\times S^5$ by exploiting the $SU(2,2|4)$ superalgebra and Cartan forms on the coset. The action combines a Born-Infeld term with a Wess-Zumino term defined via a closed 5-form $H_5$, with κ-invariance ensured by a precise choice of $H_5$ in terms of Cartan forms and the invariant field strength $F$. After gauge fixing, the theory exhibits 16 linear and 16 non-linear (conformal) supersymmetries, consistent with the $SO(4,2)\times SO(6)$ isometry and supporting a SYM effective action interpretation in the large-charge/near-horizon regime. The results provide a symmetry-based framework for D3-brane dynamics in the AdS/CFT context and set the stage for non-Abelian generalizations and gauge-fixing subtleties.

Abstract

We find the space-time supersymmetric and kappa-invariant action for a D3-brane propagating in the AdS_5 x S^5 background. As in the previous construction of the fundamental string action in this maximally supersymmetric string vacuum the starting point is the corresponding superalgebra su(2,2|4). We comment on the super Yang-Mills interpretation of the gauge-fixed form of the action.