  We develop a general framework for computing the holographic 2-point
functions and the corresponding conductivities in asymptotically locally AdS
backgrounds with an electric charge density, a constant magentic field, and
possibly non-trivial scalar profiles, for a broad class of
Einstein-Maxwell-Axion-Dilaton theories, including certain Chern-Simons terms.
Holographic renormalization is carried out for any theory in this class and the
computation of the renormalized AC conductivities at zero spatial momentum is
reduced to solving a single decoupled first order Riccati equation. Moreover,
we develop a first order fake supergravity formulalism for dyonic
renormalization group flows in four dimensions, allowing us to construct
analytically infinite families of such backgrounds by specifying a
superpotential at will. These RG flows interpolate between AdS$_4$ in the UV
and a hyperscaling violating Lifshitz geometry in the IR with exponents $1<z<3$
and $\theta=z+1$. For $1<z<2$ the spectrum of fluctuations is gapped and
discrete. Our hope and intention is that this analysis can serve as a manual
for computing the holographic 1- and 2-point functions and the corresponding
transport coefficients in any dyonic background, both in the context of AdS/CMT
and AdS/QCD.
