appear in standard ${\cal N}=8$ supergravity. In AdS$_4$ masslessness is not well characterized by the absence of a mass term in the Lagrangian but rather by the reducibility of the field representation. Representations at spin $s$ generally have dimension $2s+1$ but some special ones are reducible and allow decoupling of a ghost representation that has spin $s_{\rm ghost}=s-1$ and so dimension $2s_{\rm ghost}+1=2s-1$. This leaves two physical degrees of freedom for massless particles with spin, as expected. Group theory methods show that this reduction is possible precisely when the conformal dimension is $\Delta = s+1$ (and so $\nu = \Delta-{3\over 2} = s -\frac{1}{2}$) and also specify that the spin $s-1$ ghosts have $\Delta_{\rm ghost}=s+2$ [@Metsaev:1994ys]. These results do not strictly apply for the lowest spins $s={1\over 2}, 0$ but we can apply them formally with the understanding that the ghost subtraction in fact enhances a real scalar to a complex representation.[^4] These rules give $$\label{eq:Kbosemassless}
K^{(s, {\rm massless})}_{\rm boson}(t) = K^{(s, s+1)}_{\rm boson}(t) - K^{(s-1, s+2)}_{\rm boson}(t) = \frac{1}{16\pi^2\ell^4_A}\bigg(\frac{2\ell_A^4}{t^2} + \frac{8s^2 \ell_A^2}{t}  -5s^4 + s^2 - \frac{2}{15}\bigg)~,$$ for a massless boson with spin $s$, and $$\label{eq:Kfermimassless}
K^{(s, {\rm massless})}_{\rm fermion} = (-)\left[ K^{(s, s+1)}_{\rm fermion}(t) - K^{(s-1, s+2)}_{\rm fermion}(t) 