Comments on the symmetry of AdS 6 solutions in string/M-theory and Killing spinor equations

Abstract

It was recently pointed out in [1] that AdS6 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=5 purely bosonic non-linear sigma model action related to AdS6 in M-theory.