Safe Gauge-String Correspondence

TL;DR

This paper proposes a holographic duality between safe gauge theories, which are quantum field theories with non-Gaussian ultraviolet fixed points, and safe noncritical string theories in higher dimensions, providing new insights into their phases and nonperturbative behavior.

Contribution

It develops the 'safe' gauge-string correspondence, establishing a holographic duality for safe gauge theories with matter fields and exploring their phases and implications.

Findings

Evidence for the correspondence in theories with fermion and scalar matter.

Identification of weak and strong coupling phases with specific AdS profiles.

Proposal of safe theories as nonperturbative limits of known conformal theories.

Abstract

Safe theories are quantum field theories whose continuum limit is defined by a non-Gaussian ultraviolet fixed point when the ultraviolet cutoff is removed. They constitute an important set in the space of quantum field theories. Here we develop the `safe' gauge-string correspondence program according to which $d$-dimensional safe gauge theories, admitting the `t Hooft-Veneziano limit, are holographically dual to $(d+1)$-dimensional safe noncritical string theories on asymptotically anti-de Sitter space. We provide evidences for this correspondence on a class of safe templates that engage fermion and scalar matter fields into gauge, Yukawa and Higgs self-interactions. Safe theories can feature in the infrared both a weak coupling phase and a strong coupling phase on either side of the ultraviolet fixed point. They correspond respectively to dilaton and warp factors taking domain-wall or Liouville-wall profiles on asymptotically anti-de Sitter space. We argue that four-dimensional ${\cal N}=4$ super Yang-Mills theories and all known interacting (super)conformal field theories are nonperturbative limit situations of safe gauge theories. The weak coupling phase provides a solvable holographic renormalization group flow while the strong coupling infrared phase provides a runaway-free alternative to holographic QCD.