Abstract
We determine central charges, critical exponents and appropriate gradient flow relations for nonsupersymmetric vector-like and chiral Gauge-Yukawa theories that are fundamental according to Wilson and that feature calculable UV or IR interacting fixed points. We further uncover relations and identities among the various local and global conformal data. This information is used to provide the first extensive characterisation of general classes of free and safe quantum field theories of either chiral or vector-like nature via their conformal data. Using large $N_f$ techniques we also provide examples in which the safe fixed point is nonperturbative but for which conformal perturbation theory can be used to determine the global variation of the $a$ central charge.
Highlights
The standard model is embodied by a gauge-Yukawa theory and constitutes one of the most successful theories of nature
An important class of gauge-Yukawa theories is the one that, according to Wilson [1,2], can be defined fundamental. This means that the theories belonging to this class are valid at arbitrary short and long distances. In practice this is ensured by requiring that a conformal field theory controls the short distance behavior
Free theories are a time-honoured example [3,4] in which the ultraviolet is controlled by a not interacting conformal field theory
Summary
The standard model is embodied by a gauge-Yukawa theory and constitutes one of the most successful theories of nature. An important class of gauge-Yukawa theories is the one that, according to Wilson [1,2], can be defined fundamental This means that the theories belonging to this class are valid at arbitrary short and long distances. Free theories are a time-honoured example [3,4] in which the ultraviolet is controlled by a not interacting conformal field theory. The original model has since enjoyed various extensions by inclusion of semisimple gauge groups [6] and supersymmetry [7,8] These type of theories constitute an important alternative to asymptotic freedom. We will specialize our findings to determine the conformal data of several fundamental gauge-Yukawa theories at IR and UV interacting fixed points. In the Appendices we provide further technical details and setup notation for the perturbative version of the a-theorem and conformal perturbation theory
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