Novel solutions of RG equations for α(s) and β(α) in the large-N c limit

A general solution of RG equations in the framework of background perturbation theory is written in the large-N _c limit. A simplified (model) approximation to the general solution is suggested that allows β(α) and α(s) to be written to any loop order. The resulting α _B (Q ²) coincides asymptotically at large |Q ²| with standard (free) α _s , saturates at small Q ²≥0, and has poles at timelike Q ² in agreement with analytic properties of physical amplitudes in the large-N _c limit.

     

Dimensional crossover in the large-N limit

We consider dimensional crossover for anO(N) Landau-Ginzburg-Wilson model on ad-dimensional film geometry of thicknessL in the large-N limit. We calculate the full universal crossover scaling forms for the free energy and the equation of state. We compare the results obtained using environmentally friendly renormalization with those found using a direct, non-renormalization-group approach. A set of effective critical exponents are calculated and scaling laws for these exponents are shown to hold exactly, thereby yielding nontrivial relations between the various thermodynamic scaling functions.     

Simplified large-N limit in stochastic quantization

In the large-N limit,O(N)-invariant models become exactly soluble due to factorization properties first emphasized by Migdal and Witten. It is shown that in this limit, the Langevin equation of stochastic quantization offers a direct and simple determination of the mass gap. The method is applied to different bosonic and fermionic models.     

On the large-N limit in symplectic matrix models

We study the large-N behavior of SP(N) invariant quantum mechanical matrix models. We establish a saddle-point method through the standard collective field technique and find that it produces the correct large-N behavior. We exhibit, therefore, the semiclassical origin at the large-N limit in this model.     

Superconductivity in the t-J model in the large-N limit

Using a 1/N expansion for X-operators the leading contributions to the linearized equation for the superconducting gap of the t-J model are derived and the gap equation solved numerically on a square lattice. We find a strong instability towards superconductivity only in the d-wave (T ₃) channel with T _c/│t│ ～ 0:01 where T _c is the transition temperature and t the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term with the band width, and a retarded term due to charge and spin fluctuations with ～ J, as energy scale.     

Approaching the large-N limit: A renormalization group approach to large-N field theories

A technique is developed for finding recursive solutions to field theories that take values in SU(N). The approach can be used as a method of solving the large-N limit as well as calculating finite-N effects. This is illustrated with examples of the anharmonic oscillator, SU(N) chiral model and two-dimensional lattice QCD.     

Factorisation in large-N limit of lattice gauge theories revisited

We prove using the Schwinger-Dyson equations that the factorisation property holds for all gauge-invariant Green’s function in the large-N limit of a Wilson-Polyakov lattice gauge theory.     

Effective interactions and superconductivity in the t-J model in the large-N limit

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C_4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature T_c is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. T_c increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively. Received: 16 June 1998 / Accepted: 14 July 1998     

Hadronic decays of η and η′ in the large-N limit

Working in the large-N approximation (N being the number of colors), we relate thestrong η′→ηππ processes to theweak K _L→πππ decays. Chiral corrections are crucial to reproduce the experimental data. The isospin-violating η(η′)→πππ and the weakη→K ⁺π^- decays are also treated in this framework. We comment on the predictions of a “QCD-inspired” approach which determines in principle the chiral symmetry-breaking scales considered, and consequently the Skyrme coupling.     

The effect of shear in self-assembled fluids: The large-N limit

The dynamics of self-assembled fluids subjected to a uniform shear are solved for large-N component model of microemulsions. The dynamical structure factor S(k, t) is studied for quenches from an uncorrelated high temperature state into the Lifshitz line within the microemulsion phase. The structure factor shows multiscaling behavior with characteristic length scales (t7/ ln t)1/6 in the flow direction and (t/ ln t)1/6 in directions perpendicular to the flow. The structure factor shows two parallel ridges in the shear-flow plane.     

Delta-->Ngamma in large-N(c) QCD

The decay Delta(+)-->pgamma is studied in the 1/N(c) expansion of QCD. The ratio of the helicity amplitudes is determined to be A(3/2)/A(1/2)=sqrt[3]+O(1/N(2)(c)). Equivalently, the ratio E2/M1 of the multipole amplitudes is predicted to be order 1/N(2)(c).     

Calculation of the large-N limit of CMB anisotropies induced by global scalar fields

Usually large 3D simulations are used to calculate the cosmic microwave background anisotropies induced by global scalar fields. By going to the largeN limit and solving the equations of motion analytically, we can drastically reduce the amount of numerical computations needed, while still finding results quite similar to the corresponding functions in the texture model.     

New relations for excited baryons in large-N(c) QCD

We show that excited baryons in large-N(c) QCD form multiplets, within which masses are first split at O(1/N(c)). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/N(c) order exclusively to eta-N rather than pi-N, and vice versa for the N(1650). This multiplet structure is reproduced by a simple large-N(c) quark model, well studied in the literature, that describes resonances as single-quark excitations.     

No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.