Supersymmetric AdS_7 backgrounds in half-maximal supergravity and marginal operators of (1,0) SCFTs

TL;DR

This work maps the space of fully supersymmetric $AdS_7$ vacua in seven-dimensional half-maximal gauged supergravity and proves the absence of physical moduli for these backgrounds, implying no supersymmetric deformations preserving all supercharges. It then aligns the bulk results with the dual six-dimensional $\mathcal{N}=(1,0)$ SCFTs by showing, through representation theory of the superconformal algebra, that there are no exactly marginal operators and hence no conformal manifold. The methods rely on embedding-tensor data, gauge-group constraints, and the Goldstone/Bogomolny analysis of scalar fluctuations, highlighting a sharp dichotomy between AdS vacua and marginal deformations in this holographic setup. The results constrain the landscape of $AdS_7$ solutions and six-dimensional SCFT moduli spaces with maximal supersymmetry and offer a stringent consistency check for AdS/CFT in seven dimensions.

Abstract

We determine the supersymmetric AdS_7 backgrounds of seven-dimensional half-maximal gauged supergravities and show that they do not admit any deformations that preserve all 16 supercharges. We compare this result to the conformal manifold of the holographically dual (1,0) superconformal field theories and show that accordingly its representation theory implies that no supersymmetric marginal operators exist.