Abstract
Four-dimensional gauge theories with matter can have regions in parameter space, often dubbed conformal windows, where they flow in the infrared to nontrivial conformal field theories. It has been conjectured that conformality can be lost because of merging of two nearby fixed points that move into the complex plane, and that a walking dynamics governed by scaling dimensions of operators defined at such complex fixed points can occur. We find controlled, parametrically weakly coupled, and ultraviolet-complete 4D gauge theories that explicitly realize this scenario. We show how the walking dynamics is controlled by the coupling of a double-trace operator that crosses marginality. The walking regime ends when the renormalization group flow of this coupling leads to a (weak) first-order phase transition with Coleman-Weinberg symmetry breaking. A light dilatonlike scalar particle appears in the spectrum, but it is not parametrically lighter than the other excitations.
Highlights
Understanding the phases of gauge theories is one of the most interesting problems in high energy and condensed matter physics
It has been conjectured that conformality can be lost because of merging of two nearby fixed points that move into the complex plane, and that a walking dynamics governed by scaling dimensions of operators defined at such complex fixed points can occur
We show how the walking dynamics is controlled by the coupling of a double-trace operator that crosses marginality
Summary
Understanding the phases of gauge theories is one of the most interesting problems in high energy and condensed matter physics. Conformality loss and walking in 4D strongly coupled gauge theories are still conjectural. They should have a parameter that makes the full RG flow arbitrarily weakly coupled (to make the perturbative expansion reliable), and another one that allows us to tune from a regime with an IR CFT to a regime with complex fixed points and walking.
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