Holography with a 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 $\theta >d-1$.

arXiv comment26 pages plus appendices, 12 figures. v2: published text

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