Instabilities of weakly correlated electronic gas on a two dimensional lattice

We use the Kadanoff-Wilson renormalization group to find the instabilities of the two dimensional Hubbard model in the weak coupling limit. Starting from the full bandwidth, we reduce the energy cutoff for fermions and derive the low-energy effective action. If the filling is enough far from one half, the effective low-energy theory is BCS and there exists a mean-field like superconducting instability with D-wave order parameter. Close to the half-filling, the effective low-energy theory is parquet and the dominant fluctuations at the critical temperature are antiferromagnetic.     

Heavy-particle-induced effective lagrangian in spontaneously broken theories (II). The abelian Higgs-Kibble model

In the context of the abelian Higgs-Kibble model with a charged fermion, we study in detail low-energy effective field theories of light particles when the heavy mass scales in the theory are generated by the Higgs-Kibble mechanism. Our analysis is based on the systematic use of factorization methods, and is valid to all orders in renormalized perturbation theory. Emphasis is given to finding the vestiges of the original (spontaneously broken) local gauge symmetry left in low-energy effective field theories, and general techniques are developed for that purpose. When only Fermi fields or / and physical Higgs fields correspond to light particles, low-energy effective field theories do not exhibit such signs. On the other hand, when physical gauge fields (together with other unphysical fields) correspond to light particles, the original local gauge symmetry restricts the resulting low-energy effective local action to a non-trivial form.     

Systematic low-energy effective theory for magnons and charge carriers in an antiferromagnet

By electron or hole doping quantum antiferromagnets may turn into high-temperature superconductors. The low-energy dynamics of antiferromagnets are governed by their Nambu–Goldstone bosons—the magnons—and are described by an effective field theory analogous to chiral perturbation theory for the pions in strong interaction physics. In analogy to baryon chiral perturbation theory—the effective theory for pions and nucleons—we construct a systematic low-energy effective theory for magnons and electrons or holes in an antiferromagnet. The effective theory is universal and makes model-independent predictions for the entire class of antiferromagnetic cuprates. We present a detailed analysis of the symmetries of the Hubbard model and discuss how these symmetries manifest themselves in the effective theory. A complete set of linearly independent leading contributions to the effective action is constructed. The coupling to external electromagnetic fields is also investigated.     

Model-independent calculation of radiative neutron capture on lithium-7

The radiative neutron capture on lithium-7 is calculated model independently using a low-energy halo effective field theory. The cross section is expressed in terms of scattering parameters directly related to the S-matrix elements. It depends on the poorly known p-wave effective range parameter r(1). This constitutes the largest uncertainty in traditional model calculations. It is explicitly demonstrated by comparing with potential model calculations. A single parameter fit describes the low-energy data extremely well and yields r(1)≈-1.47 fm(-1).     

Weak interaction breakdown induced by supergravity

We show that spontaneously broken N=1 supergravity can lead to an effective low-energy theory which is phenomenologically acceptable. We study a general low-energy theory and give restrictions which its parameters must satisfy in order to lead to a breakdown of weak interactions. The naturalness condition that the low-energy superpotential be scale invariant is imposed.     

Regularization,renormalization and “peratization” in effective field theory for two nucleons

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, the renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff \( \Lambda\) as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit \( \Lambda\) \( \rightarrow\) ∞ yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.     

Possible spontaneous breaking of lorentz and CPT symmetry

One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of such effects into a low-energy effective field theory is presented. An extension of the standard model that includes Lorentz-and CPT-breaking terms is developed. The restriction of the standard model extension to the QED sector is then discussed.     

Supersymmetric Noether Currents and Seiberg–Witten Theory

The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to derive the mass-formula for the quantized Seiberg–Witten model from the supersymmetric algebra. We check that the mass-formula of the low-energy theory agrees with that of the full theory (in the broken phase).     

The Born-Infeld action from conformal invariance of the open superstring

We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of the string. Thus the bosonic part of the low-energy open superstring effective action is just that of the open bosinic string. We also that these results are exact to all loop orders of sigma-model perturbation theory.     

Soliton solutions in an effective action for SU(2) Yang—Mills theory: including effects of higher-derivative term

The Skyrme-Faddeev-Niemi (SFN) model, which is an O(3) σ model in three dimensional space, upto fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. In this paper, we derive the second-derivative term perturbatively and show that the SFN model with the second-derivative term possesses soliton solutions. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Lattice simulations for few- and many-body systems

We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory is discussed for cold atoms as well as low-energy nucleons with and without pions. A number of different lattice formulations and computational algorithms are considered, and an effort is made to show common themes in studies of cold atoms and low-energy nuclear physics as well as common themes in work by different collaborations.     

A Toy Model of the M5-Brane: Anomalies of Monopole Strings in Five Dimensions

We study a five-dimensional field theory which contains a monopole (string) solution with chiral fermion zero modes. This monostring solution is a close analog of the fivebrane solution of M-theory. The cancellation of normal bundle anomalies parallels that for the M-theory fivebrane; in particular, the presence of a Chern-Simons term in the low-energy effective U(1) gauge theory plays a central role. We comment on the relationship between the microscopic analysis of the world-volume theory and the low-energy analysis and draw some cautionary lessons for M-theory.     

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.     

Quark condensation, induced symmetry breaking and color superconductivity at high density

The phase structure of hadronic matter at high density relevant to the physics of compact stars and relativistic heavy-ion collisions is studied in a low-energy effective quark theory. The relevant phases that figure are (1) chiral condensation, (2) diquark color condensation (color superconductivity) and (3) induced Lorentz-symmetry breaking (“ISB”). For a reasonable strength for the effective four-Fermi current–current interaction implied by the low-energy effective quark theory for systems with a Fermi surface we find that the “ISB” phase sets in together with chiral symmetry restoration (with the vanishing quark condensate) at a moderate density while color superconductivity associated with scalar diquark condensation is pushed up to an asymptotic density. Consequently, color superconductivity seems rather unlikely in heavy-ion collisions although it may play a role in compact stars. Lack of confinement in the model makes the result of this analysis only qualitative but the hierarchy of the transitions we find seems to be quite robust.     

General analysis of two-body nucleon decays

An effective nucleon decay theory has been developed by Weinberg and Wilczek-Zee consistent with low-energy phenomenology. This theory, together with the SU(6) quark model, is used to derive two-body nucleon decay branching ratios. Scalar boson exchange effects are included and lead to non-trivial modifications of the pure vector boson exchange results. Contributions from both spectator and nucleon pole diagrams are considered.     

Fermi systems with strong forward scattering

We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, that is scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi-liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different 'universality classes' and discuss the behaviour of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective lowenergy theories. Particular attention is paid to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.     

Low-energy impact of a heavy Higgs boson sector

The effective theory which characterizes the low-energy sensitivity of the minimal Weinberg-Salam model to a heavy Higgs boson sector is shown to be the gauged SU(2)_L × U(1) non-linear θ model. This theory is the limit of the Weinberg-Salam model as the Higgs boson mass, M_H, is removed (M_H → ∞). Using the symmetry properties of the non-linear theory, along with a power-counting analysis, we are able to classify low-energy observables according to their sensitivity to the regulator (M_H). At one loop, the greatest sensitivity is a logarithmic dependence on the Higgs boson mass. The M_H dependent corrections to some specific, experimentally accessible observables are calculated, and other possible applications of this technique are discussed.     

The spectrum of a class of supersymmetric theories with false vacua

The spectrum of a supersymmetric quantum mechanics model, whose potential has a steep supersymmetric minimum and a broad non-supersymmetric minimum, is analyzed. With the exception of the supersymmetric ground state, the low-energy spectrum is found to be determined entirely by the non-supersymmetric well. The model is motivated by effective lagrangians proposed for supersymmetric QCD. It is speculated that in an equivalent field theory exhibiting a supersymmetric true vacuum and a non-supersymmetric false vacuum, the false vacuum can play an important rôle in the physics, and that the lowest energy excitations are extended field configurations involving a new mass scale.