Safe Gauge-String Correspondence.

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 a `safe' gauge-string correspondence program according to which a $d$-dimensional safe gauge theory, admitting the `t Hooft-Veneziano limit, is holographically dual to $(d+1)$-dimensional safe noncritical string theory 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 and a strong coupling phases on either side of the ultraviolet fixed point. They correspond respectively to dilaton and warp profiles taking the form of domain-wall or Liouville-wall on an 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 is a natural playground for the holographic renormalization group flow while the strong coupling infrared phase is a runaway-free alternative to holographic QCD.