Anisotropic gravity solutions in AdS/CMT

TL;DR

This paper constructs anisotropic gravity solutions in AdS/CMT that break Lorentz symmetry, exhibiting unique scaling behaviors and Lifshitz-like fixed points, with implications for dual field theories in various dimensions.

Contribution

It introduces new gravity solutions with anisotropic scaling symmetry, extending the AdS/CMT correspondence to non-rotational Lifshitz-like fixed points.

Findings

Solutions exhibit anisotropic scaling along temporal and spatial directions.

Dual field theories display Lifshitz-like fixed points with specific scaling exponents.

Minimum generators for Lifshitz points are identified in different dimensions.

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, $t\to \lambda^{z_1}t, x\to \lambda^{z_2}t, y\to \lambda y$, 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.