Spectral functions of gauge theories with Banks-Zaks fixed points

We investigate spectral functions of matter-gauge theories that are asymptotically free in the ultraviolet and display a Banks-Zaks conformal fixed point in the infrared. Using perturbation theory, CallanSymanzik resummations, and UV-IR connecting renormalization group trajectories, we analytically determine the gluon, quark, and ghost propagators in the entire complex momentum plane. At weak coupling, we find that a Kallen-Lehmann spectral representation of propagators is achieved for all fields, and determine suitable ranges for gauge-fixing parameters. At strong coupling, a proliferation of complex conjugated branch cuts renders a causal representation impossible. We also derive relations for scaling exponents that determine the presence or absence of propagator nonanalyticities. Further results include spectral functions for all fields up to five loop order, bounds on the conformal window, and an algorithm to find running gauge coupling analytically at higher loops. Implications of our findings and extensions to other theories are discussed.

Automated summary

We investigate the spectral functions of matter-gauge theories that exhibit an asymptotically free UV behavior and a Banks-Zaks conformal IR fixed point. The gluon, quark, and ghost propagators are analytically determined using perturbation theory, Callan-Symanzik resummations, and UV-IR connecting renormalization group trajectories. While a Kallen-Lehmann spectral representation is achieved for all fields at weak coupling, a causal representation becomes impossible at strong coupling due to the proliferation of complex conjugated branch cuts. We derive scaling exponent relations that determine the presence of propagator nonanalyticities and present additional results such as spectral functions up to five loop order, bounds on the conformal window, and an algorithm for analytically finding running gauge coupling at higher loops. The implications of our findings and possible extensions to other theories are also discussed.