Strong Coupling Dynamics Research Articles

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained.

On the strong coupling dynamics of heterotic string theory onC3/Z3

We study the strong coupling dynamics of the heterotic E_8 x E_8 string theory on the orbifolds T^6/Z_3 and C^3/Z_3 using the duality with the Horava-Witten M-theory picture. This leads us to a conjecture about the low energy description of the five dimensional E_0-theory (the CFT that describes the the singularity region of M-theory on C^3/Z_3) compactified on S^1/Z_2.

Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

We study the spontaneous breakdown of SO(10) symmetry in the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory in ten dimensions. Our analysis is based on a Gaussian expansion technique, which was originally proposed by Kabat-Lifschytz and applied successfully to the strong coupling dynamics of the Matrix Theory. We propose a prescription for including higher order corrections, which yields a rapid convergence in a simple example. This prescription is then applied to the IIB matrix model up to the third order. We find that the `self-consistency equations' allow various symmetry breaking solutions. Among them, the solution preserving SO(4) symmetry is found to have the smallest free energy. The value of the free energy comes closer to the analytic formula obtained by Krauth-Nicolai-Staudacher as we increase the order. The extent of the space-time in the 4 directions is larger than the remaining 6 directions, and the ratio increases with the order. These results provide the first analytical evidence that four-dimensional space-time is generated dynamically in the IIB matrix model.

(2,0) Superconformal OPE's in D = 6, selection rules and non-renormalization theorems

We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT$_6$ by constructing all possible three-point functions that they can form with another, in general long operator. Such three-point functions are uniquely determined by superconformal symmetry. Selection rules are derived, which allow us to infer ``non-renormalization theorems'' for an abstract superconformal field theory. The latter is supposedly related to the strong-coupling dynamics of $N_c$ coincident M5 branes, dual, in the large-$N_c$ limit, to the bulk M-theory compactified on AdS$_7 \times$S$_4$. An interpretation of extremal and next-to-extremal correlators in terms of exchange of operators with protected conformal dimension is given.

Microscopic description ofd-wave superconductivity by Van Hove nesting in the Hubbard model

We devise a computational approach to the Hubbard model that captures the strong coupling dynamics arising when the Fermi level is at a Van Hove singularity in the density of states. We rely on an approximate degeneracy among the many-body states accounting for the main instabilities of the system (antiferromagnetism, d-wave superconductivity). The Fermi line turns out to be deformed in a manner consistent with the pinning of the Fermi level to the Van Hove singularity. For a doping rate $\delta \sim 0.2$, the ground state is characterized by d-wave symmetry, quasiparticles gapped only at the saddle-points of the band, and a large peak at zero momentum in the d-wave pairing correlations.

One-scale model of dynamical supersymmetry breaking

A model of gauge-mediated supersymmetry breaking is constructed in which the low-energy physics depends on a single dynamical scale. Strong coupling dynamics of gauge theories plays an important role, in particular through its effects on beta functions and through confinement. The model does not have distinct messenger and supersymmetry-breaking sectors. The scale of supersymmetry breaking is of order 10-100 \TeV, implying that the decay of the next-to-lightest superpartner into the gravitino is prompt. Superoblique corrections are enhanced. A Dirac fermion and one complex scalar, in a 10 or \bar{10} of (global) SU(5), are predicted to be relatively light and to satisfy certain mass relations with the standard model squarks and sleptons.

Inflationary Reheating in Grand Unified Theories

Grand unified theories may display multiply interacting fields with strong coupling dynamics. This poses two new problems: (1) What is the nature of chaotic reheating after inflation, and (2) how is reheating sensitive to the mass spectrum of these theories? We answer these questions in two interesting limiting cases and demonstrate an increased efficiency of reheating which strongly enhances nonthermal topological defect formation, including monopoles and domain walls. Nevertheless, the large fluctuations may resolve this monopole problem via a modified Dvali-Liu-Vachaspati mechanism in which nonthermal destabilization of discrete symmetries occurs at reheating.

Singular Yukawa and gauge couplings in d = 4 heterotic string vacua

In this paper we discuss the singularities in the Yukawa and gauge couplings of N = 1 compactifications of the SO(32) heterotic string in four space-time dimensions. Such singularities can arise from the strong coupling dynamics of a confined non-perturbative gauge group.

M theory fivebrane interpretation for strong coupling dynamics of SO(N) gauge theories

We study M theory fivebranes to understand the moduli space of vacua of N=1 supersymmetric SO(N_c) gauge theory with N_f flavors in four dimensions. We discuss how the various branches of this theory arise in the string/M theory brane configurations and compare our results with the ones obtained earlier by Intriligator and Seiberg in the context of field theory. In the M theory approach, we explain the various branches from the asymptotic position of semi-infinite D4 branes in the $w=x^8+i x^9$ direction, which is closely related to the eigenvalues of the meson matrix $M^{ij} = Q^{i}_a Q^{j}_a$ where $Q^{i}_a$ is a squark multiplet ( $i=1, \cdots, 2N_f$ and $ a=1, \cdots, N_c$).In M theory, these branches are explained by observing a new phenomena which did not occur for the gauge groups SU(N_c) or Sp(N_c).

Simple gauge-mediated models with local minima

We describe a simple class of supersymmetric gauge theories that can act as supersymmetry-breaking sectors for gauge-mediated supersymmetry breaking. The models have a local supersymmetry-breaking minimum along a direction in field space where a singlet gets a large expectation value. The potential along this direction has a runaway behavior stabilized by supersymmetry breaking in the effective low-energy theory. The supersymmetric vacua are at infinite field values, and cosmological bounds on false vacuum decay are easily satisfied. The models have no dimensionful parameters, and all mass scales arise through strong coupling dynamics. Simple variants of the model are compatible with perturbative unification, can naturally have dynamical supersymmetry breaking at a scale as low as 10 TeV, and can solve the R axion problem without appealing to Planck-scale effects.

Strong coupling dynamics of branes from M-theory

We study some aspects of the strong coupling dynamics of Dirichlet six branes, anti- six branes, and orientifold planes by using the equivalence of type IIA string theory and M-theory on S^1. In the strong coupling limit there exists static configuration of brane and anti-brane at arbitrary separation, suspended in an external magnetic field. The mass of the open string stretched between the brane and the anti-brane approaches a finite positive value even when the branes coincide. Similar result is obtained for a Dirichlet six brane on top of an orientifold six plane. We also derive the anomalous gravitational interaction on the brane and the orientifold plane from M-theory.

Analytical study of nonlinear-optical pulse dynamics in arrays of linearly coupled waveguides

The dynamics of nonlinear pulse propagation in arrays of linearly coupled optical waveguides is considered. For an array of three waveguides, a simplified model based on a variational method is able to predict the steady-state solutions and the strong coupling dynamics with a good degree of accuracy and to furnish a necessary condition for the existence of localized states, as confirmed by numerical solutions of the governing equations. The pulse–radiation interaction is also studied, revealing that additional, long-period oscillations overlap the linear coupling frequency. In the regime of initial conditions that lead to strong localization dynamics, we present a theoretical result that predicts to a good approximation the asymptotic localized state.

New principles for string/membrane unification

The target space theory of the N = (2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either 1 + 1 or 2 + 1 dimensions. Among the target space theories in 1 + 1 dimensions are the bosonic, type II, and heterotic string world-sheet field theories in a physical gauge. The (2 + 1)-dimensional version describes a consistent quantum theory of supermembranes in 10 + 1 dimensions. The unifying framework for all of these vacua is a theory of (2 + 2)-dimensional self-dual geometries embedded in 10 + 2 dimensions. There are also indications that the N = (2,1) string describes the strong-coupling dynamics of compactifications of critical string theories to two dimensions, and may lead to insights about the fundamental degrees of freedom of the theory.

String dynamics at strong coupling

The dynamics of superstring, supergravity and M-theories and their compactifications are probed by studying the various perturbation theories that emerge in the strong and weak-coupling limits for various directions in coupling constant space. The results support the picture of an underlying non-perturbative theory that, when expanded perturbatively in different coupling constants, gives different perturbation theories, which can be perturbative superstring theories or superparticle theories. The p-brane spectrum is considered in detail and a criterion found to establish which p-branes govern the strong-coupling dynamics. In many cases there are competing conjectures in the literature, and this analysis decides between them. In other cases, new results are found. The chiral 6-dimensional theory resulting from compactifying the type IIB string on K 3 is studied in detail and it is found that certain strong-coupling limits appear to give new theories, some of which hint at the possibility of a 12-dimensional origin.

String-string duality in ten dimensions

The heterotic string occurs as a soliton of the type I superstring in ten dimensions, supporting the conjecture that these two theories are equivalent. The conjecture that the type IIB string is self-dual, with the strong coupling dynamics described by a dual type IIB theory, is supported by the occurrence of the dual string as a Ramond-Ramond soliton of the weakly coupled theory.

String theory dynamics in various dimensions

The strong coupling dynamics of string theories in dimension d ⩾ 4 are studied. It is argued, among other things, that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring, and that a recently conjectured duality between the heterotic string and Type IIA superstrings controls the strong coupling dynamics of the heterotic string in five, six, and seven dimensions and implies S-duality for both heterotic and Type II strings.

Nonperturbative enhancement of current quark masses and underlying strong-coupling dynamics in QCD

A Nambu-Jona-Lasinio (NJL) effective theory is used to demonstrate how a comparison of current quark masses obtained from hadronic physics and "effective" current quark masses, defined to be the difference between constituent masses characterizing hadronic spectroscopy and the chiral-limiting dynamical quark mass, can provide insight into the strong-coupling regime of QCD. A phenomenologically reasonable enhancement of effective current quark masses relative to actual current quark masses is shown to be indicative of near-criticality of the NJL coupling constant.

On the estimation of cross sections for the formation of triatomic collision complexes

The traditional procedure of associating the formation of a collision complex with the passage over a centrifugal potential barrier is reinvestigated. It is argued that the complex is better defined in terms of a spatially localized critical surface (or separation), such that the complex is strongly coupled, while the system is weakly elsewhere. Weak coupling implies that the rotational and vibrational energies of the diatomic fragment are, to a good approximation, conserved. Strong coupling implies that only total energy and angular momentum is conserved. Graphical methods are used to obtain upper bounds for the cross section within weak or strong coupling dynamics by optimizing the attraction within the given constraints. Results for a K + NaCl system and a O( 1D)+H 2 system are presented and compared with results of molecular dynamic simulations available in the literature. The weak coupling constraints are found to give a useful representation of the simulation data. Discontinuities in the optimal orientation of approach indicate the presence of orientational barriers.

Strong coupling dynamics of four-dimensional $N = 1$ gauge theories from M-theory fivebrane

It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N_c) gauge group and N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N_c = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.