1998/10/31 by Einan Gardi, Georges Grunberg, G. Grunberg · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary conformal field theory #Boundary value problem #Conformal map #Duality (order theory) #Infrared fixed point #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Particle physics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Renormalization group #Supersymmetry #Theoretical physics #hep-ph #hep-th
paper · pdf · doi:10.1088/1126-6708/1999/03/024
published as JHEP 9903:024,1999 · Journal version
openalex publication_date 1999/03/30 · arxiv created 1999/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In both QCD and supersymmetric QCD (SQCD) with Nf flavors there are conformal windows where the theory is asymptotically free in the ultraviolet while the infrared physics is governed by a non-trivial fixed-point. In SQCD, the lower Nf boundary of the conformal window, below which the theory is confining is well understood thanks to duality. In QCD there is just a sufficient condition for confinement based on superconvergence. Studying the Banks-Zaks expansion and analyzing the conditions for the perturbative coupling to have a causal analyticity structure, it is shown that the infrared fixed-point in QCD is perturbative in the entire conformal window. This finding suggests that there can be no analog of duality in QCD. On the other hand in SQCD the infrared region is found to be strongly coupled in the lower part of the conformal window, in agreement with duality. Nevertheless, we show that it is possible to interpolate between the Banks-Zaks expansions in the electric and magnetic theories, for quantities that can be calculated perturbatively in both. This interpolation is explicitly demonstrated for the critical exponent that controls the rate at which a generic physical quantity approaches the fixed-point.