The AdS/CFT correspondence has sparked opportunities to study strongly coupled quantum field theories and has many applications to condensed matter physics. Gravity duals of compressible phases of matter, characterized by a dynamical critical exponent z and a hyperscaling violation (HSV) parameter theta have been constructed within a class of Einstein gravity plus matter theories.These models suffer from an embarrassment of riches, allowing too many values of z, and theta.

The work presented here, done in collaboration with A.W. Peet, considers the addition of curvature squared corrections to the usual holographic model. Working from a bottom-up perspective, we nd the ingredients necessary in order to support HSV solutions. We show that by applying standard energy conditions from gravitational physics we can constrain the z, theta parameter ranges.

Furthermore, holographic HSV solutions generally display peculiar singularity behaviour. We will discuss how introducing certain curvature squared terms can help resolve these singularities.