Supersymmetric AdS $$_6$$ 6 solutions of type IIB supergravity

We study the general requirement for supersymmetric AdS $$_6$$ solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the canonical form of the solutions. Our result agrees precisely with the work of Apruzzi et al. (JHEP 1411:099, 2014), which used the pure spinor technique. Hoping to identify the geometry of the problem, we also computed four-dimensional theory through the dimensional reduction of type IIB supergravity on AdS $$_6$$ . This effective action is essentially a non-linear sigma model with five scalar fields parametrizing $$\text {SL}(3,\mathbb {R})/\text {SO}(2,1)$$ , modified by a scalar potential and coupled to Einstein gravity in Euclidean signature. We argue that the scalar potential can be explained by a subgroup CSO(1,1,1) $$\subset \text {SL}(3,\mathbb {R})$$ in a way analogous to gauged supergravity.