Logarithmic curvature correction to Lifshitz and hyperscaling violation geometries

Abstract

In this note we consider the logarithmic curvature correction to Lifshitz and hyper scaling violation geometries. We investigate the effect of this correction to the gauge kinetic function f and the effective potential V . For the case of hyper scaling violating we show that the coupling between dilaton and the correction terms exhibit the logarithmic behavior for dilaton like for the case of squared curvature correction. We find the unexpected form of gauge kinetic function and potential in the presence of logarithmic terms. We try to resolve the IR singularity of Lifshitz and hyperscaling violation geometries by adding the logarithmic term.