Anisotropic gravity solutions in AdS/CMT

Abstract

We have constructed gravity solutions by breaking the Lorentzian symmetry to its subgroup, which means there is Galilean symmetry but without the rotational and boost invariance. This solution shows anisotropic behavior along both the temporal and spatial directions as well as among the spatial directions and more interestingly, it displays the precise scaling symmetry required for metric as well as the form fields. From the field theory point of view, it describes a theory which respects th5Ae scaling symmetry, $t\to λ^{z_1}t, x\to λ^{z_2}t, y\to λy$, for $z_1\neq z_2$, as well as the translational symmetry associated to both time and space directions, which means we have found a non-rotational but Lifshitz-like fixed points from the dual field theory point of view. We also discuss the minimum number of generators required to see the appearance of such Lifshitz points. In 1+1 dimensional field theory, it is 3 and for 2+1 dimensional field theory, the number is 4.