Holography with a Landau pole

TL;DR

This paper explores holography for gauge theories with a Landau pole, revealing how UV singularities influence physical properties and demonstrating a method to perform holographic renormalization despite UV incompleteness.

Contribution

It introduces a way to implement holographic renormalization for UV-incomplete theories using analytic continuation, and analyzes the effects of a Landau pole on holographic duals.

Findings

Holographic renormalization can be performed via analytic continuation.

UV singularity leads to a repulsive gravitational potential at high energies.

Negative specific heat appears at temperatures near the Landau pole.

Abstract

Holography for UV-incomplete gauge theories is important but poorly understood. A paradigmatic example is $d=4$, $\mathcal{N}=4$ super Yang-Mills coupled to $N_f$ quark flavors, which possesses a Landau pole at a UV scale $\Lambda_{LP}$. The dual gravity solution exhibits a UV singularity at a finite proper distance along the holographic direction. Despite this, holographic renormalization can be fully implemented via analytic continuation to an AdS solution. The presence of a UV cut-off manifests itself in several interesting ways. At energies $E \ll \Lambda_{LP}$ no pathologies appear, as expected from effective field theory. In contrast, at scales $E \lesssim \Lambda_{LP}$ the gravitational potential becomes repulsive, and at temperatures $T \lesssim \Lambda_{LP}$ the specific heat becomes negative. Although we focus on $\mathcal{N}=4$ super Yang-Mills with flavor, our qualitative results apply to a much more general class of theories, since they only depend on the fact that the metric near the UV singularity is a hyper-scaling violating metric with exponent $\theta > d-1$.