Holographic Lifshitz flows

TL;DR

This paper investigates holographic models of Lifshitz RG flows, demonstrating how Lorentz invariance can emerge dynamically in the IR from Lorentz-violating UV fixed points, with implications for strongly coupled theories.

Contribution

It introduces a minimal holographic model that efficiently captures the emergence of Lorentz invariance and constructs a line of Lifshitz fixed points with varying scaling.

Findings

Larger UV dynamical exponent z_{UV} accelerates Lorentz symmetry recovery in IR.

A line of fixed points with different Lifshitz scalings is explicitly realized.

The a-function is monotonic along all studied Lorentz-violating RG flows.

Abstract

Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or `Lifshitz') exponent $z$. Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as the flow from a $z=1$ UV fixed point to a $z=2$ IR fixed point. In strongly coupled theories, there are good arguments suggesting that Lorentz invariance can emerge dynamically in the IR from a Lorentz violating UV. In this work, we perform a generic study of fixed points and the possible RG flows among them in a minimal bottom-up holographic model without Lorentz invariance, aiming to shed light on the possible options and the related phenomenology. We find: i) A minor generalization of previous models involving a massive vector field with allowed self-couplings leads to a much more efficient emergence of Lorentz invariance than in the previous attempts. Moreover, we find that generically the larger is the UV dynamical exponent $z_{UV}$ the faster is the recovery of Lorentz symmetry in the IR. ii) We construct explicitly a holographic model with a line of fixed points, realizing different Lifshitz scaling along the line. iii) We also confirm the monotonicity of a recently proposed a-function along all our Lorentz violating RG flows.