  We analyze properties of field theories dual to extremal black branes in
(4+1) dimensions with anisotropic near-horizon geometries. Such gravity
solutions were recently shown to fall into nine classes which align with the
Bianchi classification of real three-dimensional Lie algebras. As a warmup we
compute constraints on critical exponents from energy conditions in the bulk
and scalar two point functions for a general type I metric, which has
translation invariance but broken rotations. We also comment on the divergent
nature of tidal forces in general Bianchi-type metrics. Then we come to our
main focus: extremal branes whose near-horizon isometries are those of the
Heisenberg algebra (type II). We find hyperscaling-violating solutions with
type II isometries in (4+1)-dimensions. We show that scale invariant
(4+1)-dimensional type II metrics are related by Kaluza-Klein reduction to more
symmetric $AdS_2\times R^2$ and (3+1)-dimensional hyperscaling-violating
spacetimes. These solutions generically have $\theta \leq 0$. We discuss how
one can obtain flows from UV CFTs to Bianchi-type spacetimes in the IR via the
Higgs mechanism, as well as potential inhomogeneous instabilities of type II.
Finally, we compute two-point functions of massive and massless scalar
operators in the dual field theory and find that they exhibit the behavior of a
theory with Landau levels.
