Spatially Modulated Instabilities of Geometries with Hyperscaling Violation

We perform a study of possible instabilities of the infrared AdS2 x R2 region of solutions to Einstein-Maxwell-dilaton systems which exhibit an intermediate regime of hyperscaling violation and Lifshitz scaling. Focusing on solutions that are magnetically charged, we probe the response of the system to spatially modulated fluctuations, and identify regions of parameter space in which the infrared AdS2 geometry is unstable to perturbations. The conditions for the existence of instabilities translate to restrictions on the structure of the gauge kinetic function and scalar potential. In turn, these can lead to restrictions on the dynamical critical exponent z and on the amount of hyperscaling violation theta. Our analysis thus provides further evidence for the notion that the true ground state of `scaling’ solutions with hyperscaling violation may be spatially modulated phases.