Holography with a Landau pole

Abstract

Holography for UV-incomplete gauge theories is important but poorly understood. A paradigmatic example is d = 4, N= 4 super Yang-Mills coupled to Nf quark flavors, which possesses a Landau pole at a UV scale ΛLP. 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 ≪ ΛLP no pathologies appear, as expected from effective field theory. In contrast, at scales E ≲ ΛLP the gravitational potential becomes repulsive, and at temperatures T ≲ ΛLP the specific heat becomes negative. Although we focus on 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 θ > d − 1.