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     

Effective actions for statistical data assimilation

Data assimilation is a problem in estimating the fixed parameters and state of a model of an observed dynamical system as it receives inputs from measurements passing information to the model. Using methods developed in statistical physics, we present effective actions and equations of motion for the mean orbits associated with the temporal development of a dynamical model when it has errors, there is uncertainty in its initial state, and it receives information from noisy measurements. If there are statistical dependences among errors in the measurements they can be included in this approach.     

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.     

Nuclear forces and currents in large-N C QCD

Expression of the nucleon-nucleon interaction to leading order in 1/N _C in terms of Fermi invariants allows a dynamical interpretation of the interaction and a consistent construction of the associated interaction currents. The numerically significant components of 4 different modern realistic phenomenological interaction models admit very similar meson exchange interpretations in the large-N _C limit. The ratio of the volume integrals of the leading, next-to-leading and next-to-next leading-order terms in these interaction models is roughly , which corresponds fairly well to the ratios of 1/N _C ² between the terms that would be suggested by the 1/N _C expansion if N _C = 3.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.30.Cb Nuclear forces in vacuum     

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.     

Effective actions from block diagonalization in lattice gauge theories

It is shown that the first step in Wilson's real space renormalization program for lattice gauge theories — namely the integration of internal degrees of freedom within one block — can be performed for “block-diagonalized” actions, which possess the proper continuum limit, just like the Wilson action. As a result, we obtain, on a lattice with double lattice spacing, an effective action which contains in the weak-coupling limit, in addition to the familiar plaquette terms, planar Wilson loops with six and eight links.     

Effective actions of intersecting brane worlds, fluxes and gaugino condensation

In this article we will first discuss the construction of brane world models being built either by intersecting D6-branes in type IIA orientifolds or, in the T-dual mirror picture, by D3- plus D7-branes with f-flux in type IIB orientifolds. We will show how their effective action is obtained by the calculation of scattering amplitudes between open and closed string states on intersecting D6-branes respectively on D3- and D7-branes. Secondly, turning on type IIB 3-form fluxes we will compute the induced soft supersymmetry breaking terms for the matter fields, like gaugino and scalar field masses. Finally, we will discuss the generation of 3-form flux in type IIB supergravity, which can be associated to the dynamical formation of a gaugino condensate in the confining phase of the dual N=1^* gauge theory. To cite this article: D. Lüst, C. R. Physique 5 (2004).

Résumé

Dans cet article nous discutons tout d'abord la construction de modèles de monde branaires construits soit par intersection de branes D6 dans des orientifolds de type IIA ou, dans la représentation T-duale, par des branes de type D3 et D7 avec des flux f dans les orientifolds de type IIB. Nous montrons comment obtenir leurs actions effectives en calculant les amplitudes de diffusion sur des intersections de branes de D6 et aussi sur des branes de type D3 et D7. Ensuite, nous allumons des flux pour la 3-forme de type IIB et nous calculons les termes de brisure douce de la supersymétrie pour les champs de matière, comme les masses du jaugino et des champs scalaires. Enfin, nous discutons la génération de flux pour la 3-forme de type IIB en supergravité, qui peut-être associée à la dynamique de la formation de condensat de jaugino dans la phase confinante de la théorie de jauge duale N=1^*. Pour citer cet article : D. Lüst, C. R. Physique 5 (2004).     

Master variables and spectrum equations in large-N theories

Based on the loop-space effective action approach to the large-N limit, we consider the issue of constrained minimization and the problem of small fluctuations. The master variables are introduced to allow for an unconstrained minimization; the second derivative of the effective loop-space action with respect to these variables leads to master equations for the spectrum of particle states. We show that even though these variables contain redundant degrees of freedom, the only additional eigenvalues are of zero energy. We also establish a simplification through use of a reduced ansatz.     

Effective actions for scalars and spinors in a general Robertson-Walker universe

The effective actions for massless scalars and spinors in a four-dimensional conformally flat spacetime are found. The cross term due to interaction with external gauge field is integrable and induces asymptotic freedom for the gauge coupling constant.     

Molecular binding in the large-N expansion

We apply the large-N expansion to the H⁺₂ ion. An interesting complication occurs in the leading order to yield a degenerate ground state. We also estimate the ground state energy of the hydrogen molecule using the same technique.     

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.     

The large-N magnetization in matrix models revisited

Summary We analyse the large-N limit of a matrix model with quartic self-interaction and external scalar field, by the technique of orthogonal polynomials. The rise of a ?spontaneous magnetization? is studied and compared with the previous known results, based on saddle point integration or Schwinger-Dyson equations. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Summing large-N towers in colour flow evolution

We consider soft-gluon evolution in the colour flow basis. We give explicit expressions for the colour structure of the (one-loop) soft anomalous dimension matrix for an arbitrary number of partons, and we show how the successive exponentiation of classes of large- \(N\) contributions can be achieved to provide a systematic expansion of the evolution in terms of colour-suppressed contributions.