Vacua of M-theory and string theory

TL;DR

The authors show that maximally supersymmetric vacua in M-theory and IIB string theory, namely $AdS_4\times S^7$, $AdS_7\times S^4$, and $AdS_5\times S^5$, remain exact when all higher-dimension, supersymmetric corrections are included. They employ a superspace formalism and rely on 32 unbroken supersymmetries to prove that the relevant superfields are covariantly constant, preventing any corrections to the equations of motion. The work provides a unified description of these backgrounds as fixed points in superspace and extends to a detailed superspace characterization of new supergeometries, showing that the standard AdS compactifications are robust against quantum and stringy corrections. This has implications for the stability of AdS/CFT constructions and suggests that the fluxes and scales fixed by these brane near-horizon geometries are exact features of the underlying theories.

Abstract

We argue that supersymmetric higher-dimension operators in the effective actions of M-theory and IIB string theory do not affect the maximally supersymmetric vacua: $adS_4\times S^7$ and $adS_7\times S^4$ in M-theory and $adS_5\times S^5$ in IIB string theory. All these vacua are described in superspace by a fixed point with all components of supertorsion and supercurvature being supercovariantly constant. This follows from 32 unbroken supersymmetries and allows us to prove that such vacua are exact.