Comments on the symmetry of AdS6 solutions in string/M-theory and Killing spinor equations

It was recently pointed out in [1] that AdS(6) solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to D = 4 internal space leads to a nonlinear sigma model with target SL(3, R)/SO(2, 1). We continue to study the purely bosonic D = 4 effective action, and elucidate how the addition of scalar potential term still allows Killing spinor equations in the absence of gauge fields. In particular, the potential turns out to be a single diagonal component of the coset representative. Furthermore, we perform a general analysis of the integrability conditions of Killing spinor equations and establish that the effective action can be in fact generalized to arbitrary sizes and signatures, e.g. with target SL(n, R)/SO(p, n - p) and the scalar potential expressible by a single diagonal component of the coset representative. We also comment on a similar construction and its generalizations of effective D = 5purely bosonic non-linear sigma model action related to AdS6in M-theory. (C) 2016 The Author(s). Published by Elsevier B.V.