We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed. PACS: 11.10.Hi, 11.15.-q, 11.38.Bx.

The increased interest in non-Abelian gauge theories has in recent years led to the computation of many higher-order Feynman diagrams. ' " Asymptotic form-factor and scattering amplitude calculations are of special interest, because they suggest that it might be possible to sum up diagrams with arbitrary numbers of soft gluons just as one can sum up soft-photon processes in QED. In such a progr...

It is shown that static purely electric or purely magnetic abelian field configurations in Yang-Mills theory are unstable when the electric or magnetic field strength is too large over too wide a region. The critical parameter is gEL2 (gBL2) where E (B) is a measure of the field strength, and L is a measure of the distance over which such field strengths extend.

Let G be a group and CayP (G) < Sym(G) be the subgroup of all permutations that induce graph automorphisms on every Cayley graph of G. The group G is graphically abelian if the map ν : g → g−1 belongs to CayP (G); these groups have been classified. Also G is irregular if there exists σ ∈ CayP (G) such that σ = 1G, σ(1) = 1 and σ = ν. We show G is irregular if and only if G = Dic(A, I); every no...

In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs. phase transition). To this end we consider the basic N = 2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N f = N flavors of fundamental matter (quarks). The Fayet–Iliopoulos term ξ triggers the squark condensation...

Leptin’s theorem asserts that a locally compact group is amenable if and only if its Fourier algebra has a bounded (by one) approximate identity. In the language of locally compact quantum groups—in the sense of J. Kustermans and S. Vaes—, it states that a locally compact group is amenable if and only if its quantum group dual is co-amenable. It is an open problem whether this is true for gener...

Using as a flavor symmetry a finite nonabelian dicyclic Q2N group, we show how to derive quark mass matrices with two arrangements of symmetric texture zeros which are phenomenologically viable. Three other such acceptable textures in the recent literature are unattainable in this approach and hence disfavored. We assume massive vector-like fermions and Higgs singlets transforming as judiciousl...

Let G be a non-abelian finite group. In this paper, we prove that Γ(G) is K4-free, if and only if G ∼= A× P , where A is an abelian group, P is a 2-group and G/Z(G) ∼= Z2 × Z2. Also, we show that Γ(G) is K1,3-free if and only if G ∼= S3, D8 or Q8.

A static, spherically symmetric and purely magnetic solution of the Einstein-YangMills-Dilaton theory, found previously by numerical integration is shown to obey a system of first order Bogomol’nyi equations. As common for such equations, there is a tight relation to supersymmetry, in the present case to the N=4 gauged SU(2)×SU(2) supergravity of Freedman and Schwarz. Specifically, the dilaton ...

We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our algebras become simple and purely infinite, and consequently our algebras are either purely infinite or AF-embeddable when they are simple.