Super M-brane actions in adS_4 x S^7 and adS_7 x S^4

TL;DR

The paper derives the full M-brane worldvolume actions in the near-horizon backgrounds $\{adS_4\times S^7, adS_7\times S^4\}$ to all orders in $\theta$ using only 11D supergravity torsion/curvature constraints, avoiding supercoset constructions. It provides both M2 and M5 actions, including a covariant PST-based M5 action, and proves $\kappa$-invariance in backgrounds with vanishing gravitino and covariantly constant flux, while establishing agreement with prior coset-based results (dWPPS). A killing-spinor gauge dramatically simplifies the geometric superfields, enabling explicit forms such as $E^{\bar{m}}=dx^m + \bar{\lambda} \Gamma^m d\lambda$ and $E=(-g_{00})^{-1/4} f^+(\xi) d\lambda$, and reveals that gauge fixing yields worldvolume superconformal theories: $OSp(4|8)$ for M2 and $OSp(6,2|4)$ for M5. The work thus provides a covariant, constraint-based route to M-brane dynamics in AdS backgrounds and strengthens the bridge to AdS/CFT via non-linear worldvolume superconformal actions.

Abstract

The world-volume action of the M2 brane and the M5-brane in an adS_4 x S^7 and a adS_7 x S^4 background is derived to all orders in anticommuting superspace coordinates. Contrary to recent constructions of super p-brane actions relying on supercoset methods, we only use 11 dimensional supergravity torsion and curvature constraints. Complete agreement between the two methods is found. The simplification of the actions by choosing a suitable kappa-gauge is discussed.