In Lorentzian AdS space there are both normalizable and non normalizable solutions and we also know (at least for scalar fields in bulk) what do they correspond to in the boundary. But I saw the calculation only for scalar fields. Can someone please give me a reference where people have calculated these modes for a gauge fields, say for a graviton field? McGreevy's lecture note says the relation $\Delta(\Delta-D)=m^2L^2$ gets modified to $(\Delta+j)(\Delta+j-D)=m^2L^2$ for form $j$ fields. Does this mean for other fields too the normalizable and non normalizable behavior remains the same: namely $Z_0^{\Delta_+}$ and $Z_0^{\Delta_-}$, as $z_0\rightarrow 0$ ($\Delta_{\pm}$ are two solutions of course)? How can that be?

# [Physics] Normalizable and non normalizable modes of gauge fields in AdS/CFT

string-theory

## Best Answer

At the end of Sec 3.3.1 of the MAGOO review (hep-th/9905111) you will find a useful list of the relationship between conformal dimension $\Delta$ and masses $m$ for scalars, spinors, vectors, p-forms, first order (d/2)-forms, spin $3/2$ and massless spin $2$ fields along with a list of references to the literature where these various cases were analyzed.