The paper by Shamit Kachru, Xiao Liu, and Michael Mulligan explores the gravitational duals of scale-invariant but non-Lorentz invariant fixed points in condensed matter systems, specifically those with a dynamical critical exponent \( z \). These theories, characterized by anisotropic scaling \( t \rightarrow \lambda^z t \), \( x \rightarrow \lambda x \), are of interest in the context of strongly correlated electron systems and quantum critical points in materials. The authors focus on the case where \( z = 2 \), which is relevant for multicritical points in certain magnetic materials and liquid crystals. The paper begins by introducing the concept of dynamical scaling and the Lifshitz field theory, which exhibits this scaling behavior. The authors then derive gravitational solutions that can serve as duals to these theories, using a 4D gravity with a negative cosmological term and additional \( p \)-form gauge fields. These solutions are designed to support metrics that geometrically realize the symmetries of the Lifshitz-like fixed points. Next, the authors compute two-point correlation functions for the simplest scaling operators, which are dual to free bulk scalar fields. Unlike in conformal field theories, these correlators contain more information than just the scaling dimension of the operator, including non-trivial scaling functions. They find that the correlation functions exhibit novel behavior, such as spatially localized terms, which are forbidden in Lorentz invariant theories. The paper also discusses the holographic renormalization group (RG) flows between the Lifshitz-like fixed points and conventional conformal field theories. The authors show that relevant perturbations in the gravitational duals can induce RG flows from the UV (at large \( r \)) to the IR (at small \( r \)), leading to a flow towards an \( AdS_4 \)-like spacetime. Numerical solutions suggest that the marginal direction at the Lifshitz fixed point becomes relevant at the nonlinear level. Finally, the authors outline future directions for research, including the computation of more complex observables and higher-point correlation functions, as well as the study of Wilson loops. The work provides a step towards making useful dual descriptions of critical points in condensed matter systems.The paper by Shamit Kachru, Xiao Liu, and Michael Mulligan explores the gravitational duals of scale-invariant but non-Lorentz invariant fixed points in condensed matter systems, specifically those with a dynamical critical exponent \( z \). These theories, characterized by anisotropic scaling \( t \rightarrow \lambda^z t \), \( x \rightarrow \lambda x \), are of interest in the context of strongly correlated electron systems and quantum critical points in materials. The authors focus on the case where \( z = 2 \), which is relevant for multicritical points in certain magnetic materials and liquid crystals. The paper begins by introducing the concept of dynamical scaling and the Lifshitz field theory, which exhibits this scaling behavior. The authors then derive gravitational solutions that can serve as duals to these theories, using a 4D gravity with a negative cosmological term and additional \( p \)-form gauge fields. These solutions are designed to support metrics that geometrically realize the symmetries of the Lifshitz-like fixed points. Next, the authors compute two-point correlation functions for the simplest scaling operators, which are dual to free bulk scalar fields. Unlike in conformal field theories, these correlators contain more information than just the scaling dimension of the operator, including non-trivial scaling functions. They find that the correlation functions exhibit novel behavior, such as spatially localized terms, which are forbidden in Lorentz invariant theories. The paper also discusses the holographic renormalization group (RG) flows between the Lifshitz-like fixed points and conventional conformal field theories. The authors show that relevant perturbations in the gravitational duals can induce RG flows from the UV (at large \( r \)) to the IR (at small \( r \)), leading to a flow towards an \( AdS_4 \)-like spacetime. Numerical solutions suggest that the marginal direction at the Lifshitz fixed point becomes relevant at the nonlinear level. Finally, the authors outline future directions for research, including the computation of more complex observables and higher-point correlation functions, as well as the study of Wilson loops. The work provides a step towards making useful dual descriptions of critical points in condensed matter systems.