1/N topological expansion for lattice QCD

A U(N_c) gauge theory with a global U(N_f) flavor symmetry is investigated in the limit both N_c and N_f large with the ratio ξ ≡ N_f/N_c fixed.     

Migdal approximation and 1/N expansion in QCD

We show that the Migdal approximation for the renormalization group in gauge theories in exact in the leading order in $\text{1}\text{N}$, above a critical value of the coupling constant. A systematic expansion in $\text{1}\text{N}$ is proposed. The string tension is calculated in the leading order in $\text{1}\text{N}$ in a theory without fermions.     

Strong coupling 1/N c expansion in the gluonic sector of lattice QCD: The next order

Continuing our previous work we determined the gluonic vacuum state up to sixth order and the lowest states with external quark-antiquark and (unscreened) gluon-gluon sources up to fourth order in the strong coupling 1/N _c expansion on the lattice. Unlike previously, we used here the colour electric flux operators on the links to define the colour electric energy. Additional remarks concerning the screening of external gluon sources and the analytic continuation toN _c =3 and zero lattice spacing are also included.     

Instantons and the 1/N expansion

We show that a non-interacting gas of instantons, gives a contribution which vanishes, in QCD, exponentially withN(the number of colours). If we include some of the interactions between instantons, then the resulting dilute gas of instantons—which is now in the form that is used in practice to investigate the structure of hadrons—gives a contribution that is essentialyconstant withN. Thus it is entirely consistent for both theN → ∞ limit to be useful and for the dilute gas of instantons to be relevant for the properties of hadrons.     

Nonperturbative expansion in QCD

The purpose of this article is to construct the nonperturbative expansion in quantum chromodynamics using a new small parameter and apply it to the investigation of the connection between nonperturbative and perturbative regimes of the effective coupling constant. We calculate the nonperturbative renormalization group β-function and discuss the properties of the series convergence using the two-loop approximation in this method. Based on the information from meson spectroscopy we derive the effective coupling constant in the perturbative region.     

Photoproduction of positive-parity excited baryons in the 1/Nc expansion of QCD

We analyze the photoproduction helicity amplitudes for positive-parity excited baryons in the context of the 1/N(c) expansion of QCD. The results show that subleading corrections in 1/N(c) are important and that, while one-body effective operators are dominant, there is some evidence for the need for two-body effects.     

Chiral gauge theories in the 1/N expansion

We study the large-N limit of various (SU(N) gauge theories with chiral fermion content. Assuming that the leading N → ∞ behavior is given by a sum of planar diagrams, we find that the gauge interactions must fail to confine color in some models. Other models, assuming both a planar diagram limit and confinement, must contain massless composite fermions.     

The γ function in the 1/N f expansion

The Callan-Symanzik γ-function is studied in the large number of lepton (in QED) or flavour (in QCD) limit. We have computed analytically 7 terms and they show a striking factorization. We have computed numerically 19 terms and they show a large radius of convergence and two unambiguous zeros within the region of convergence.