No light dilaton in gauge theories

We study the dynamical breakdown of approximate scale invariance in gauge theories with slowly varying couplings and without ultraviolet cutoff. We isolate the high energy contribution to the dilaton mass and obtain an expression for it in terms of the fermion self-energy Σ(k). Σ(k) is determined via an analytical treatment of the linearized, ladder Schwinger-Dyson equation. We find that this contribution to the dilaton mass is large and is surprisingly insensitive to the β-function when the β-function is small. The result is that for a technicolor theory with a slowly varying coupling there is no light dilaton. At most there is a massive scalar, the analog of the standard Higgs scalar, with a mass tied to the technifermion mass scale.     

On the confining potential in 4D SU(N_{\mathrm c}) gauge theory with dilaton

Using the formal analogy between the Dick superstring inspired model and the problem of the building of an Eguchi–Hanson metric in 4D N = 2 harmonic superspace (HS), we derive a general formula for the quark–quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton–gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10D type IIB superstring requirements. Others features are also discussed. Received: 23 December 1999 / Published online: 6 March 2000     

Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.     

Finite-size effects due to Goldstone particles in lattice gauge theory

We study the finite-size effects associated with the appearance of a light, i.e. Goldstone, particle in the Kogut-Susskind lattice gauge theory. We analytically study the order parameter $\text{(}\text{X}\text{X)}$ and the two-meson propagator in the strong coupling limit on a finite lattice. We give their explicit interpolations between the broken phase of the infinite-volume limit and the symmetric one of the finite system. We argue that the results obtained in the strong coupling limit are more general.     

Linear dilaton conformal field theory: a generalization

We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable us to study a more general case. Various properties of the model such as OPEs, central charge, conformal properties of the fields and associated algebras will be studied.     

Determination of a gauge transformation group in gauge field theory

The existence of different types of gauge transformations in gauge theory and the theory of gravitation is established and they are defined in the language of fiber bundles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 52–57, December, 1984.     

Anatomy of a gauge theory

We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson–Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov–Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.     

Spin and isospin in a gauge theory with monopoles

The mechanism by which systems of spinless bosons with isospin and spinless magnetic monopoles acquire a spin in their ground states is investigated in the context of SU(2) gauge models. Contrary to recent claims, it is demonstrated that isospin degrees of freedom are not converted into spin degrees of freedom. For a spin $\text{1}\text{2}$ state, solutions are explicitly constructed, exhibiting the isospin degree of freedom.     

Zwanziger-Landau gauge in regularized gauge theory

The Green functions of Zwanziger-gaugefixed and continuum-regularized gauge theory are finite and transverse to all orders as the Zwanziger parameter α goes to zero.     

Self-dual monopoles in a seven-dimensional gauge theory

The existence of self-dual or anti-self-dual monopoles of a seven-dimensional generalized Yang-Mills-Higgs theory is proved using the second-order equations of motion. The behavior of solutions can be used to recognize self- or anti-self-duality. Moreover, it is shown that, in the class of the field configurations under discussion, the solutions are, in fact, unique.     

High-energy scattering in a two-dimensional gauge theory

We study high-energy scattering in two-dimensional quantum chromodynamics in the 1/N_colour expansion. To first order, high-energy forward scattering amplitudes are power-behaved with the factorization, signature and exchange degeneracy properties found in dual Regge models. Backward scattering has deviations from naive quark power-counting rules which are related to the form factor and “Regge” behaviours. In the second order of 1/N_colour vacuum exchange diagrams do not give a new Pomeron singularity, but do break exchange degeneracy.     

Electric and magnetic polarizabilities of pointlike spin-1/2 particles

The electric and magnetic polarizabilities of pointlike spin-1/2 particles with an anomalous magnetic moment (AMM) are calculated by the transformation of an initial Hamiltonian into the Foldy-Wouthuysen (FW) representation. Corresponding results for spin-1/2 and spin-1 particles are compared.